TSTP Solution File: SWW244+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW244+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 23:21:31 EDT 2022
% Result : Timeout 300.02s 300.42s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWW244+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.14 % Command : bliksem %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % DateTime : Sat Jun 4 16:49:18 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.98/1.63 *** allocated 10000 integers for termspace/termends
% 0.98/1.63 *** allocated 10000 integers for clauses
% 0.98/1.63 *** allocated 10000 integers for justifications
% 0.98/1.63 *** allocated 15000 integers for termspace/termends
% 0.98/1.63 *** allocated 22500 integers for termspace/termends
% 0.98/1.63 *** allocated 33750 integers for termspace/termends
% 0.98/1.63 Bliksem 1.12
% 0.98/1.63
% 0.98/1.63
% 0.98/1.63 Automatic Strategy Selection
% 0.98/1.63
% 0.98/1.63 *** allocated 50625 integers for termspace/termends
% 0.98/1.63 *** allocated 75937 integers for termspace/termends
% 0.98/1.63 *** allocated 113905 integers for termspace/termends
% 0.98/1.63
% 0.98/1.63 Clauses:
% 0.98/1.63
% 0.98/1.63 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.98/1.63 { ! class_Rings_Oidom( t_a ), ! v_c____ = c_Groups_Ozero__class_Ozero( t_a
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Rings_Oidom( t_a ), ! skol2 = c_Groups_Ozero__class_Ozero( t_a )
% 0.98/1.63 }.
% 0.98/1.63 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a,
% 0.98/1.63 c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) ), skol2 ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.98/1.63 { ! class_Rings_Oidom( t_a ), ! skol3 = c_Groups_Ozero__class_Ozero( t_a )
% 0.98/1.63 }.
% 0.98/1.63 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a, v_p ), skol3
% 0.98/1.63 ) = c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.98/1.63 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.98/1.63 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.98/1.63 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.98/1.63 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.63 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.98/1.63 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.98/1.63 c_Polynomial_Odegree( X, Y ) ) }.
% 0.98/1.63 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 0.98/1.63 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 0.98/1.63 ( t_a ), ! skol4 = c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.98/1.63 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 0.98/1.63 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 0.98/1.63 ( t_a ), ! v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.63 t_a ) ), c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If(
% 0.98/1.63 tc_Nat_Onat, c_fequal( skol28, c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( t_a ) ) ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.98/1.63 ), c_Nat_OSuc( c_Polynomial_Odegree( t_a, skol28 ) ) ), skol23 ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 0.98/1.63 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 0.98/1.63 ( t_a ), v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a
% 0.98/1.63 ) ), c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If(
% 0.98/1.63 tc_Nat_Onat, c_fequal( skol28, c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( t_a ) ) ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.98/1.63 ), c_Nat_OSuc( c_Polynomial_Odegree( t_a, skol28 ) ) ), skol23 ) ) =
% 0.98/1.63 c_Nat_OSuc( c_Polynomial_Odegree( t_a, v_cs____ ) ) }.
% 0.98/1.63 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 0.98/1.63 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 0.98/1.63 ( t_a ), hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( t_a ), Y ), skol23 ) ), hAPP(
% 0.98/1.63 c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, skol4, skol28 ) ), Y )
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha1( X, Y ), alpha23
% 0.98/1.63 ( X, Y ) }.
% 0.98/1.63 { ! alpha1( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.63 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! alpha23( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.63 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! alpha23( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! alpha23( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha23( X, Y ) }.
% 0.98/1.63 { ! alpha1( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! alpha1( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 0.98/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha2( X, Y ), alpha24( X
% 0.98/1.63 , Y ) }.
% 0.98/1.63 { ! alpha2( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! alpha24( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! alpha24( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! alpha24( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha24( X, Y ) }.
% 0.98/1.63 { ! alpha2( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 0.98/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.98/1.63 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.98/1.63 .
% 0.98/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.98/1.63 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.98/1.63 .
% 0.98/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.98/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.98/1.63 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.63 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.98/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.63 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.63 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.98/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.98/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.98/1.63 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.98/1.63 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.98/1.63 c_Polynomial_Odegree( X, Z ) ) }.
% 0.98/1.63 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.98/1.63 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.98/1.63 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.98/1.63 { ! c_Nat_OSuc( X ) = X }.
% 0.98/1.63 { ! X = c_Nat_OSuc( X ) }.
% 0.98/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.98/1.63 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.98/1.63 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.98/1.63 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.98/1.63 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.98/1.63 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.98/1.63 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.98/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.98/1.63 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.98/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.98/1.63 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.98/1.63 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.63 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.63 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.98/1.63 ( tc_Nat_Onat ) ) = X }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ), X ) = X }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.63 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.98/1.63 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), !
% 0.98/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.98/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.98/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.98/1.63 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.98/1.63 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.98/1.63 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.98/1.63 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.98/1.63 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.98/1.63 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.98/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.98/1.63 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Nat_Onat, Z, Y ) ) }.
% 0.98/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.63 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.63 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Oidom( t_a ), ! v_c____ = c_Groups_Ozero__class_Ozero( t_a
% 0.98/1.63 ), ! skol5 = c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.98/1.63 { ! class_Rings_Oidom( t_a ), ! v_c____ = c_Groups_Ozero__class_Ozero( t_a
% 0.98/1.63 ), ! c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ), c_Nat_OSuc(
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If( tc_Nat_Onat, c_fequal(
% 0.98/1.63 skol29, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Nat_OSuc(
% 0.98/1.63 c_Polynomial_Odegree( t_a, skol29 ) ) ), skol24 ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Rings_Oidom( t_a ), ! v_c____ = c_Groups_Ozero__class_Ozero( t_a
% 0.98/1.63 ), c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ), c_Nat_OSuc(
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If( tc_Nat_Onat, c_fequal(
% 0.98/1.63 skol29, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Nat_OSuc(
% 0.98/1.63 c_Polynomial_Odegree( t_a, skol29 ) ) ), skol24 ) ) = c_Nat_OSuc(
% 0.98/1.63 c_Polynomial_Odegree( t_a, c_Polynomial_OpCons( t_a, v_c____, v_cs____ )
% 0.98/1.63 ) ) }.
% 0.98/1.63 { ! class_Rings_Oidom( t_a ), ! v_c____ = c_Groups_Ozero__class_Ozero( t_a
% 0.98/1.63 ), hAPP( c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, v_c____,
% 0.98/1.63 v_cs____ ) ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( t_a ),
% 0.98/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( t_a ), X ), skol24 ) ), hAPP(
% 0.98/1.63 c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, skol5, skol29 ) ), X )
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.63 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.63 .
% 0.98/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.63 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.98/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.63 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.98/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.98/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.98/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.98/1.63 ) ) }.
% 0.98/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.98/1.63 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.98/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.63 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.63 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.63 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.98/1.63 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.63 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.63 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.63 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.63 ), ! U = T }.
% 0.98/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.63 ), ! Z = Y }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.98/1.63 ) ), Z ) }.
% 0.98/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.63 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.63 ), U = Z, T = Y }.
% 0.98/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.63 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.63 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.98/1.63 ( X ) }.
% 0.98/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.98/1.63 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.98/1.63 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.63 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.98/1.63 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.98/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.98/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.98/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.98/1.63 .
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.98/1.63 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.98/1.63 ) ), T ), Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.63 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.98/1.63 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.63 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.98/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.98/1.63 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.98/1.63 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.98/1.63 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.63 }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.98/1.63 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.98/1.63 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.98/1.63 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.63 = Y }.
% 0.98/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.63 = Y }.
% 0.98/1.63 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.63 = Y }.
% 0.98/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.63 = Y }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.98/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.98/1.63 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.63 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.63 = Y }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.63 = Y }.
% 0.98/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.63 = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.98/1.63 tc_Nat_Onat ) ) = Y }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.98/1.63 tc_Nat_Onat ) ) = Y }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.98/1.63 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.63 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.63 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.98/1.63 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.63 , Y ), X ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.98/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.98/1.63 tc_Nat_Onat ) }.
% 0.98/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.98/1.63 tc_Nat_Onat ) }.
% 0.98/1.63 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.63 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.63 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.98/1.63 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.98/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.63 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.63 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.63 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.63 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.98/1.63 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.98/1.63 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.63 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.98/1.63 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 T, Y ), Z = Y }.
% 0.98/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 T, Y ) }.
% 0.98/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 Y, Z ), T = Y }.
% 0.98/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 Y, Z ) }.
% 0.98/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 T, Y ), Z = Y }.
% 0.98/1.63 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 T, Y ), Z = Y }.
% 0.98/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 Y, T ), Z = Y }.
% 0.98/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.98/1.63 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.98/1.63 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.98/1.63 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.98/1.63 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.98/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.98/1.63 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.98/1.63 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.98/1.63 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.98/1.63 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.98/1.63 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.98/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.98/1.63 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.98/1.63 X, Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.98/1.63 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.98/1.63 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.98/1.63 , Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.98/1.63 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.98/1.63 }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.98/1.63 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.98/1.63 ) }.
% 0.98/1.63 { c_Nat_Onat_Onat__size( c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Nat_Onat, c_Nat_Onat_Onat__size( X ), c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.98/1.63 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.98/1.63 ( X ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.98/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.98/1.63 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.98/1.63 .
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.98/1.63 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.98/1.63 .
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.63 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.63 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.63 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.63 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.63 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.63 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.98/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.98/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.63 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 0.98/1.63 ), Y ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.98/1.63 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.98/1.63 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.98/1.63 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.98/1.63 c_Polynomial_Ocoeff( X, Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.98/1.63 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.98/1.63 ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.98/1.63 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.98/1.63 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol6( X
% 0.98/1.63 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol6( X, Y, Z ) ), Z = Y
% 0.98/1.63 }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.98/1.63 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.98/1.63 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.63 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.63 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.98/1.63 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.98/1.63 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 = Y }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.63 ( X ) }.
% 0.98/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.63 , Y ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.63 = Y }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.63 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.98/1.63 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.63 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.63 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.63 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.63 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.63 ( X, Y ) ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.63 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.63 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.63 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.63 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.98/1.63 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.63 ) ), Y ) }.
% 0.98/1.63 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.98/1.63 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.63 ( X, Y ) ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.98/1.63 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.98/1.63 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.63 Y ) ) = Y }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 Z, Y ) ) = Y }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.98/1.63 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.98/1.63 c_Polynomial_Odegree( X, Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.98/1.63 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.98/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.98/1.63 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.98/1.63 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.98/1.63 .
% 0.98/1.63 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.63 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.63 Z ) = Y }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.63 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.63 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.98/1.63 ( X, Y ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 X ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.98/1.63 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.98/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.98/1.63 Y ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.63 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ) ) = Z }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.63 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.98/1.63 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.63 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.98/1.63 , Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.98/1.63 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.63 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.98/1.63 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.98/1.63 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.98/1.63 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.98/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.98/1.63 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.98/1.63 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.63 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.98/1.63 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.98/1.63 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.98/1.63 c_Polynomial_Odegree( X, Y ) }.
% 0.98/1.63 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.98/1.63 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.98/1.63 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.98/1.63 ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.98/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.98/1.63 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.63 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.98/1.63 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.98/1.63 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.98/1.63 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.98/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.98/1.63 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.98/1.63 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.98/1.63 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.63 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.63 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.63 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.98/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.98/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.98/1.63 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.63 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.98/1.63 ( X, Z ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.63 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 0.98/1.63 tc_Nat_Onat, X ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.63 ) ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.63 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.98/1.63 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.63 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.98/1.63 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.98/1.63 Y ) ) ), Y ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.98/1.63 Y ) ) ), Y ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.98/1.63 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.98/1.63 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.63 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.98/1.63 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.98/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.98/1.63 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.98/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.98/1.63 c_Polynomial_OpCons( X, T,
% 0.98/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.98/1.63 .
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.98/1.63 .
% 0.98/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.98/1.63 .
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.63 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.63 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 0.98/1.63 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.98/1.63 ( tc_Int_Oint ) }.
% 0.98/1.63 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.63 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.63 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.63 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.63 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.63 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.63 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.63 Z, T ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Int_Oint ), X ) = X }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.98/1.63 ( tc_Int_Oint ) ) = X }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.98/1.63 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.63 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.63 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.63 , Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.63 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.98/1.63 , Z, Y ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.63 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.63 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.98/1.63 }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.63 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.98/1.63 }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.63 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.98/1.63 }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.63 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.98/1.63 }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.98/1.63 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.98/1.63 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.98/1.63 X, T, Z ), Y ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.98/1.63 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.63 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.98/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.98/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.98/1.63 ( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.98/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 0.98/1.63 c_Polynomial_Odegree( X, Z ) }.
% 0.98/1.63 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha3( X
% 0.98/1.63 , Y, T ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha25( X
% 0.98/1.63 , Y, Z, T ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! alpha3( X, Y, T ), ! alpha25( X, Y, Z, T )
% 0.98/1.63 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.98/1.63 ( X, T, Z ), Y ) }.
% 0.98/1.63 { ! alpha25( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.98/1.63 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha25( X, Y, Z, T ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha25( X
% 0.98/1.63 , Y, Z, T ) }.
% 0.98/1.63 { ! alpha3( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.98/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha3( X
% 0.98/1.63 , Y, Z ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.98/1.63 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.63 , Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.98/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.98/1.63 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.63 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.63 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.98/1.63 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.63 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 X ) }.
% 0.98/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.98/1.63 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.98/1.63 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.98/1.63 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.98/1.63 hAPP( Z, skol7( U, W, Z ) ) ) }.
% 0.98/1.63 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.98/1.63 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol7( X
% 0.98/1.63 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.98/1.63 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.98/1.63 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol25( X,
% 0.98/1.63 Y, Z ) ) ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Z, Y ), alpha56( X, Y, Z, T ), ! Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Z, Y ), alpha56( X, Y, Z, T ), ! hAPP(
% 0.98/1.63 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.98/1.63 .
% 0.98/1.63 { ! alpha56( X, Y, Z, T ), alpha58( X, Y, Z, T ), alpha53( X, Y, T ) }.
% 0.98/1.63 { ! alpha56( X, Y, Z, T ), alpha58( X, Y, Z, T ), ! hAPP(
% 0.98/1.63 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! alpha58( X, Y, Z, T ), alpha56( X, Y, Z, T ) }.
% 0.98/1.63 { ! alpha53( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.98/1.63 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 alpha56( X, Y, Z, T ) }.
% 0.98/1.63 { ! alpha58( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.63 ( X ), Z, T ), alpha59( X, Y, Z, T ) }.
% 0.98/1.63 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha58( X, Y
% 0.98/1.63 , Z, T ) }.
% 0.98/1.63 { ! alpha59( X, Y, Z, T ), alpha58( X, Y, Z, T ) }.
% 0.98/1.63 { ! alpha59( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.98/1.63 ), skol8( X, Y, U, W ), Y ) }.
% 0.98/1.63 { ! alpha59( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.98/1.63 ), skol8( X, Y, U, T ), T ) }.
% 0.98/1.63 { ! alpha59( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.63 ( X ), skol8( X, Y, Z, T ), Z ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha59( X, Y
% 0.98/1.63 , Z, T ) }.
% 0.98/1.63 { ! alpha53( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! alpha53( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha53( X, Y, Z
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.63 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.98/1.63 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.98/1.63 { c_HOL_Obool_Obool__size( c_fTrue ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ) }.
% 0.98/1.63 { c_HOL_Obool_Obool__size( c_fFalse ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.98/1.63 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.63 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.63 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.98/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.98/1.63 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.98/1.63 ) ) }.
% 0.98/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.63 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.98/1.63 .
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.63 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.63 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.63 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.63 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.98/1.63 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.98/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.98/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.98/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.98/1.63 , Y ) ) = Y }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.98/1.63 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.98/1.63 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.98/1.63 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.98/1.63 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.63 = Y }.
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.98/1.63 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.63 ( X ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.98/1.63 X, Y ) ) = Y }.
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.63 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.98/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.63 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.98/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.63 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.98/1.63 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.63 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.98/1.63 ) ), Y ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.63 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.63 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.63 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.63 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.63 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Int_Oint, Y, X ) }.
% 0.98/1.63 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.63 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.63 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.63 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.63 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.63 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.98/1.63 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.63 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.98/1.63 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.98/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.98/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.63 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.98/1.63 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.98/1.63 ) ), Z ) }.
% 0.98/1.63 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.63 Z ) ), U ), T ) = Y }.
% 0.98/1.63 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.63 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), Z ), U ), Y ) }.
% 0.98/1.63 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.63 W ) ), U ), Y ) }.
% 0.98/1.63 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.63 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), Z ), U ), Y ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.63 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.63 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.98/1.63 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.63 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.63 Z ) ), Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.63 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.98/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.98/1.63 }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.63 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.98/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.98/1.63 }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.63 X, Y ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.63 X, Z, Y ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.98/1.63 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.98/1.63 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.63 , Y ) ) }.
% 0.98/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.63 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.63 X, Y ) ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.98/1.63 , Z ), X ) ), T ) ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Int_Oint, U, T ) ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.98/1.63 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.98/1.63 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.98/1.63 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.63 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.63 X ) ) }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.63 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Y ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.63 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.98/1.63 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.98/1.63 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.98/1.63 .
% 0.98/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.98/1.63 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.98/1.63 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.98/1.63 tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.98/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.63 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.98/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.98/1.63 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.98/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.98/1.63 ( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.63 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.98/1.63 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.63 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.98/1.63 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.63 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.63 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.98/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.98/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.63 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Nat_Onat, Z, X ) }.
% 0.98/1.63 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.98/1.63 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha4( X, Y ), Y = X }
% 0.98/1.63 .
% 0.98/1.63 { ! alpha4( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! alpha4( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! alpha4( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), alpha4( X, Y ) }.
% 0.98/1.63 { ! alpha5( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! alpha5( X, Y ), ! Y = X }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha5( X, Y ) }
% 0.98/1.63 .
% 0.98/1.63 { ! alpha5( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! alpha5( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), alpha5( X, Y ) }.
% 0.98/1.63 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.63 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.63 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Nat_Onat, Y, Z ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.63 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Nat_Onat, Y, Z ) }.
% 0.98/1.63 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.98/1.63 , Z ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.98/1.63 Z, Y ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Nat_Onat, Y, Z ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.63 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.98/1.63 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.98/1.63 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.63 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.98/1.63 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ) ) }.
% 0.98/1.63 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.98/1.63 tc_Nat_Onat ), X ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.63 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.63 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.98/1.63 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.63 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.63 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.98/1.63 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.98/1.63 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.98/1.63 = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Int_Oint, Z, X ) }.
% 0.98/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.98/1.63 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.98/1.63 ) }.
% 0.98/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.63 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.98/1.63 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.63 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.98/1.63 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.98/1.63 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.98/1.63 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.98/1.63 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 0.98/1.63 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.98/1.63 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.98/1.63 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.98/1.63 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.98/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.98/1.63 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, Z ) ), T ) =
% 0.98/1.63 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.63 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.63 Y ) ), c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus
% 0.98/1.63 ( X, Y, Z ), T ) ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.98/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.63 X ) ) }.
% 0.98/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.98/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.63 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.98/1.63 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.63 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.63 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Y, Z ) }.
% 0.98/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.98/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.63 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.63 ) }.
% 0.98/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.63 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.63 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.98/1.63 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.98/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.63 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.63 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.98/1.63 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.98/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.63 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.98/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.63 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.98/1.63 , Y, Z ) ) }.
% 0.98/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.98/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.63 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.98/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.98/1.63 , Y, Z ) ) }.
% 0.98/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.98/1.63 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha6( X, Y, Z ), alpha26( X, Y
% 0.98/1.63 , Z ) }.
% 0.98/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha6( X, Y, Z
% 0.98/1.63 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.63 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha26( X, Y, Z
% 0.98/1.63 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.63 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.63 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.63 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.63 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.63 ), alpha26( X, Y, Z ) }.
% 0.98/1.63 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.63 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.63 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.63 ), alpha6( X, Y, Z ) }.
% 0.98/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha7( X, Y, Z ), alpha27
% 0.98/1.64 ( X, Y, Z ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha7( X, Y, Z
% 0.98/1.64 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha27( X, Y, Z
% 0.98/1.64 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.64 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 ), alpha27( X, Y, Z ) }.
% 0.98/1.64 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.64 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.64 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.64 ), alpha7( X, Y, Z ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 Z, Y ) ), alpha28( X, Y, Z, T ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 Z, Y ) ), alpha41( X, Y, Z, T ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha28( X, Y, Z
% 0.98/1.64 , T ), ! alpha41( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.64 { ! alpha41( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), alpha47( X, Y, Z, T ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.64 , alpha41( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha47( X, Y, Z, T ), alpha41( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha47( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha47( X, Y, Z, T ), alpha8( X, Y, T ) }.
% 0.98/1.64 { ! alpha51( X, Y, Z, T ), ! alpha8( X, Y, T ), alpha47( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha51( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.64 alpha51( X, Y, Z, T ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha51( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha28( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 alpha28( X, Y, Z, T ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha28( X, Y, Z, T )
% 0.98/1.64 }.
% 0.98/1.64 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.64 , alpha8( X, Y, Z ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.64 , alpha8( X, Y, Z ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.64 Z ), Y ), alpha29( X, Y, Z, T ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.64 Z ), Y ), alpha42( X, Y, Z, T ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha29( X, Y, Z
% 0.98/1.64 , T ), ! alpha42( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.98/1.64 { ! alpha42( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), alpha48( X, Y, Z, T ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.64 , alpha42( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha48( X, Y, Z, T ), alpha42( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha48( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha48( X, Y, Z, T ), alpha9( X, Y, Z ) }.
% 0.98/1.64 { ! alpha52( X, Y, Z, T ), ! alpha9( X, Y, Z ), alpha48( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha52( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.64 alpha52( X, Y, Z, T ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha52( X, Y, Z, T )
% 0.98/1.64 }.
% 0.98/1.64 { ! alpha29( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.64 alpha29( X, Y, Z, T ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha29( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.64 , alpha9( X, Y, Z ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.64 , alpha9( X, Y, Z ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 Z, Y ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.64 Y ), Z ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.64 Y ), Z ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 Z, Y ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 Z, Y ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.64 Y ), Z ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.64 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.64 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.98/1.64 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.98/1.64 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.64 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.98/1.64 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.64 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.64 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.64 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.64 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.64 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.64 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.64 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.98/1.64 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.64 ), Y ) }.
% 0.98/1.64 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.64 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.98/1.64 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.64 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, Z, Y ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.98/1.64 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, Z, Y ) }.
% 0.98/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.64 , T ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.64 , T, Y ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.64 , Y, T ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.64 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, Z, Y ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.64 , T, Y ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, T, Y ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.64 , Y, Z ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.64 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.64 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.64 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.64 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.64 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.64 ( X, Y ), Z ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.64 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.64 ( X, Z ), Y ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.64 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.98/1.64 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.98/1.64 .
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), X ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.64 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.98/1.64 }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.98/1.64 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.64 X ) ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.98/1.64 .
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.98/1.64 .
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.98/1.64 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.98/1.64 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.64 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.64 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.64 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.98/1.64 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.98/1.64 .
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.64 .
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.64 .
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.64 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.98/1.64 , X ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.64 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.64 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.98/1.64 ( X ), Z, Y ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.64 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.98/1.64 { alpha54( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.98/1.64 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.64 { alpha54( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.98/1.64 ( X, Y ), Z ) ) }.
% 0.98/1.64 { ! alpha54( X, Y, Z ), alpha57( X, Y, Z ), Z = Y }.
% 0.98/1.64 { ! alpha54( X, Y, Z ), alpha57( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.98/1.64 ) ) }.
% 0.98/1.64 { ! alpha57( X, Y, Z ), alpha54( X, Y, Z ) }.
% 0.98/1.64 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha54( X, Y, Z ) }.
% 0.98/1.64 { ! alpha57( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.98/1.64 }.
% 0.98/1.64 { ! alpha57( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.98/1.64 X, Y ), Z ) ), alpha57( X, Y, Z ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.64 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.64 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.98/1.64 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, Y, Z ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.64 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.64 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.64 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.64 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.98/1.64 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 }.
% 0.98/1.64 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.98/1.64 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.64 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.64 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.98/1.64 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.98/1.64 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha30( X, Y, Z, T ) }.
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha10( X, Y, Z ) }.
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha30( X, Y, Z, T ), !
% 0.98/1.64 alpha10( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.98/1.64 { ! alpha30( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.98/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.98/1.64 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha30( X, Y, Z, T ) }.
% 0.98/1.64 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha30(
% 0.98/1.64 X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha10( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { Z = c_Groups_Ozero__class_Ozero( X ), alpha10( X, Y, Z ) }.
% 0.98/1.64 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha10( X, Y, Z ) }.
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha31( X, Y, Z, T ) }.
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha11( X, Y, T ) }.
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha31( X, Y, Z, T ), !
% 0.98/1.64 alpha11( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.64 { ! alpha31( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.98/1.64 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha31( X, Y, Z, T ) }.
% 0.98/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha31(
% 0.98/1.64 X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha11( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { Y = c_Groups_Ozero__class_Ozero( X ), alpha11( X, Y, Z ) }.
% 0.98/1.64 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha11( X, Y, Z ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.98/1.64 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.98/1.64 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.98/1.64 ( X ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.98/1.64 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.98/1.64 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.64 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.64 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.98/1.64 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.98/1.64 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.98/1.64 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 0.98/1.64 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.64 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.64 Y ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X )
% 0.98/1.64 , Y ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.98/1.64 .
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( X ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.64 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.98/1.64 .
% 0.98/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.98/1.64 .
% 0.98/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( X ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( X ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha12( X, Y, Z, T ),
% 0.98/1.64 alpha32( X, Y, Z, T ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha12( X, Y, Z, T ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha32( X, Y, Z, T ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.64 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha32( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.98/1.64 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.98/1.64 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha12( X, Y, Z, T ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha13( X, Y, Z, T ),
% 0.98/1.64 alpha33( X, Y, Z, T ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha13( X, Y, Z, T ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha33( X, Y, Z, T ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! alpha33( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! alpha33( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha33( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.64 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.64 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha13( X, Y, Z, T ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.64 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.98/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.64 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.98/1.64 ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.64 ) ) }.
% 0.98/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( X ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.64 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , Z, Y ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.64 .
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.64 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.64 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 , Y ) }.
% 0.98/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.64 , Y ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.64 .
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.64 ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.64 .
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( X ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.98/1.64 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.98/1.64 .
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.98/1.64 , Y ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.98/1.64 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.98/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha14( X, Y ) }.
% 0.98/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.64 { ! alpha14( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.64 c_Nat_OSuc( X ) ) }.
% 0.98/1.64 { ! alpha14( X, Y ), Y = c_Nat_OSuc( skol9( Z, Y ) ) }.
% 0.98/1.64 { ! alpha14( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol9( X,
% 0.98/1.64 Y ), X ) }.
% 0.98/1.64 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.98/1.64 ), alpha14( X, Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol10( X ) ) }.
% 0.98/1.64 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.98/1.64 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol11( X, Y ) ) ) }.
% 0.98/1.64 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.64 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.64 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.64 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.64 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.64 tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.98/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.98/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.64 Y ), X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), Z ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.98/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.98/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.64 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.64 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.64 ), X ) ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.64 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Nat_Onat, Z, X ), Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.64 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.98/1.64 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.98/1.64 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.98/1.64 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.64 ), X ) ) }.
% 0.98/1.64 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.98/1.64 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.98/1.64 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.98/1.64 .
% 0.98/1.64 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.98/1.64 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.98/1.64 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.98/1.64 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.98/1.64 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.98/1.64 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.98/1.64 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.98/1.64 }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.98/1.64 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.98/1.64 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.98/1.64 .
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.64 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.98/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.98/1.64 .
% 0.98/1.64 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.64 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.98/1.64 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.98/1.64 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.64 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 , c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.98/1.64 .
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.64 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.64 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.98/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.64 X, W, Z ) ), U ), T ), Y ) }.
% 0.98/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.64 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.64 ( X ), Z ), U ), Y ) ) }.
% 0.98/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.98/1.64 ( X, Z, W ) ), U ), Y ) ) }.
% 0.98/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.98/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.64 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.98/1.64 ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T, Z ), Y ) =
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.98/1.64 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Polynomial_Osmult( X,
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.64 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ),
% 0.98/1.64 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y )
% 0.98/1.64 ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.98/1.64 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.98/1.64 ) ) = X }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.98/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.64 , alpha15( X, Y, Z ) }.
% 0.98/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.64 , alpha34( X, Y, Z ) }.
% 0.98/1.64 { ! alpha15( X, Y, Z ), ! alpha34( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.64 { ! alpha34( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.64 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.64 { ! hBOOL( hAPP( Z, skol12( T, U, Z ) ) ), alpha34( X, Y, Z ) }.
% 0.98/1.64 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol12( X, Y, Z ) ),
% 0.98/1.64 alpha34( X, Y, Z ) }.
% 0.98/1.64 { ! alpha15( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.98/1.64 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha15( X, Y, Z ) }
% 0.98/1.64 .
% 0.98/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha15
% 0.98/1.64 ( X, Y, Z ) }.
% 0.98/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.64 , ! alpha16( X, Y, Z ) }.
% 0.98/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.64 , ! alpha35( X, Y, Z ) }.
% 0.98/1.64 { alpha16( X, Y, Z ), alpha35( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.64 { ! alpha35( X, Y, Z ), ! hBOOL( hAPP( Z, skol13( T, U, Z ) ) ) }.
% 0.98/1.64 { ! alpha35( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.64 skol13( X, Y, Z ) ) }.
% 0.98/1.64 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.98/1.64 ) ), alpha35( X, Y, Z ) }.
% 0.98/1.64 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.98/1.64 }.
% 0.98/1.64 { ! alpha16( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ) ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16( X, Y, Z ) }.
% 0.98/1.64 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.98/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.98/1.64 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.98/1.64 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.98/1.64 ( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.98/1.64 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.98/1.64 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.98/1.64 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.98/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.98/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.98/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.98/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.64 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), Y ) }.
% 0.98/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.64 ), X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.64 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 X ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.98/1.64 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.64 ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.64 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 X ) }.
% 0.98/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 0.98/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.98/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.64 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.64 tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.98/1.64 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.98/1.64 tc_Int_Oint, Z, Y ), X ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.98/1.64 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.98/1.64 tc_Int_Oint, Z, X ), Y ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.64 tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.98/1.64 .
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.64 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.64 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.64 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.64 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol14( X, Y ) ) }.
% 0.98/1.64 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.98/1.64 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.64 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol15( X, Y ) ) }.
% 0.98/1.64 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.98/1.64 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.98/1.64 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.98/1.64 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 0.98/1.64 .
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.64 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.98/1.64 ( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.64 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.64 ( tc_Int_Oint, Y ), X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.98/1.64 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.98/1.64 }.
% 0.98/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.98/1.64 ( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.64 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.98/1.64 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.64 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), c_Rings_Odvd__class_Odvd
% 0.98/1.64 ( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ) }
% 0.98/1.64 .
% 0.98/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus
% 0.98/1.64 ( tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y )
% 0.98/1.64 = c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) ), Y ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.98/1.64 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Int_Oint, Y, X ), X ) }.
% 0.98/1.64 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.98/1.64 ( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.98/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.64 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.98/1.64 = X }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.64 tc_Int_Oint ) ) ) }.
% 0.98/1.64 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.64 tc_Int_Oint ) ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.98/1.64 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.98/1.64 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.98/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.64 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.98/1.64 alpha17( X, Y, Z ) }.
% 0.98/1.64 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.98/1.64 alpha36( X, Y, Z ) }.
% 0.98/1.64 { ! alpha17( X, Y, Z ), ! alpha36( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.64 { ! alpha36( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.64 alpha43( X, Y, Z ) }.
% 0.98/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha36( X, Y, Z ) }.
% 0.98/1.64 { ! alpha43( X, Y, Z ), alpha36( X, Y, Z ) }.
% 0.98/1.64 { ! alpha43( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.98/1.64 ), alpha49( X, Y, Z, T ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol16( X, T, U ), X ),
% 0.98/1.64 alpha43( X, Y, Z ) }.
% 0.98/1.64 { ! alpha49( X, Y, Z, skol16( X, Y, Z ) ), alpha43( X, Y, Z ) }.
% 0.98/1.64 { ! alpha49( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.98/1.64 hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.64 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol17( X, Y, T ) ), T
% 0.98/1.64 ), alpha49( X, Y, Z, T ) }.
% 0.98/1.64 { ! hBOOL( hAPP( Z, T ) ), alpha49( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha17( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.64 hBOOL( hAPP( Z, Y ) ) }.
% 0.98/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha17( X, Y, Z ) }.
% 0.98/1.64 { ! hBOOL( hAPP( Z, Y ) ), alpha17( X, Y, Z ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.98/1.64 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X )
% 0.98/1.64 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.64 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.64 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.98/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.64 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.98/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.98/1.64 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.98/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.98/1.64 X, Z, Y ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.64 }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.98/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.64 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.64 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.64 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.98/1.64 , Y ) ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.98/1.64 ), Z ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.98/1.64 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.98/1.64 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.98/1.64 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.64 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.64 ( X, Z, Y ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.98/1.64 ( X, Y, Z ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.64 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.98/1.64 , Y ) ), Y ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.64 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.98/1.64 ), Z ), Y ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.64 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.98/1.64 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.98/1.64 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.64 T, Z ), Y ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.98/1.64 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.64 T, Y ), Z ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.98/1.64 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.98/1.64 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.98/1.64 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.98/1.64 ), Z ) }.
% 0.98/1.64 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.98/1.64 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.98/1.64 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.98/1.64 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.98/1.64 , U ), Z ) }.
% 0.98/1.64 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.98/1.64 Y ) ), Y ) }.
% 0.98/1.64 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.98/1.64 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.98/1.64 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.98/1.64 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.98/1.64 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.98/1.64 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.64 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.98/1.64 , Y ) ), Y ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.64 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 0.98/1.64 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.64 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.64 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.64 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 0.98/1.64 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.64 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.64 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 0.98/1.64 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.98/1.64 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.64 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 0.98/1.64 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.64 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 0.98/1.64 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 0.98/1.64 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 0.98/1.64 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 0.98/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 0.98/1.64 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.64 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.98/1.64 }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.64 , alpha44( X, Y, Z, T ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha44( X, Y, Z, T ),
% 0.98/1.64 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.98/1.64 { ! alpha44( X, Y, Z, T ), alpha18( X, Z, T ) }.
% 0.98/1.64 { ! alpha44( X, Y, Z, T ), alpha37( X, Y, T ) }.
% 0.98/1.64 { ! alpha18( X, Z, T ), ! alpha37( X, Y, T ), alpha44( X, Y, Z, T ) }.
% 0.98/1.64 { ! alpha37( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ), alpha45( X, Y, Z ) }.
% 0.98/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha37( X
% 0.98/1.64 , Y, Z ) }.
% 0.98/1.64 { ! alpha45( X, Y, Z ), alpha37( X, Y, Z ) }.
% 0.98/1.64 { ! alpha45( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.64 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.98/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha45( X
% 0.98/1.64 , Y, Z ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.98/1.64 ), c_Polynomial_Odegree( X, Z ) ), alpha45( X, Y, Z ) }.
% 0.98/1.64 { ! alpha18( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.64 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha18( X,
% 0.98/1.64 Y, Z ) }.
% 0.98/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha18( X
% 0.98/1.64 , Y, Z ) }.
% 0.98/1.64 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.98/1.64 .
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.64 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 0.98/1.64 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.98/1.64 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.64 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.64 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.98/1.64 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.98/1.64 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.64 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.98/1.64 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.98/1.64 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.98/1.64 ) }.
% 0.98/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.98/1.64 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 0.98/1.64 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 0.98/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.64 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.64 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.98/1.64 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.64 alpha19( X, Y, Z ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.64 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! alpha19( X, Y, Z ),
% 0.98/1.64 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.98/1.64 { ! alpha19( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.64 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.64 alpha19( X, Y, Z ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.64 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.64 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.98/1.64 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.98/1.64 .
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.64 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.64 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.64 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.98/1.64 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.98/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.98/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.64 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.64 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.98/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Int_Oint ) ) = X }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.98/1.64 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( X ) }.
% 0.98/1.64 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.98/1.64 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.64 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.64 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.64 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Int_Oint ), Y ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.64 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.98/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.64 ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.64 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, Z, Y ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.64 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 0.98/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 0.98/1.64 }.
% 0.98/1.64 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.98/1.64 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.64 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.98/1.64 , Z ) ) }.
% 0.98/1.64 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.98/1.64 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 0.98/1.64 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.98/1.64 , Z ) ) }.
% 0.98/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.64 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.98/1.64 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.98/1.64 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.64 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.98/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z, Y )
% 0.98/1.64 ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.98/1.64 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.98/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.98/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.98/1.64 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.98/1.64 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.98/1.64 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.98/1.64 ) }.
% 0.98/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.98/1.64 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.98/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.30/1.64 }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.30/1.64 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oabs__class_Oabs( X, Y ) ) }
% 1.30/1.64 .
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.30/1.64 ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.30/1.64 ), c_Rings_Odvd__class_Odvd( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) }
% 1.30/1.64 .
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oabs__class_Oabs( X, Z )
% 1.30/1.64 = c_Groups_Oabs__class_Oabs( X, Y ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.30/1.64 }.
% 1.30/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y ) )
% 1.30/1.64 = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X, Y )
% 1.30/1.64 ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 1.30/1.64 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 1.30/1.64 ) }.
% 1.30/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.30/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), c_Groups_Oabs__class_Oabs
% 1.30/1.64 ( tc_Int_Oint, Y ) = c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) }.
% 1.30/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.30/1.64 tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) =
% 1.30/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.30/1.64 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) = c_Groups_Oone__class_Oone
% 1.30/1.64 ( tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, X,
% 1.30/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.30/1.64 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 1.30/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.30/1.64 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.30/1.64 ( hAPP( c_Power_Opower__class_Opower( X ),
% 1.30/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) =
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.30/1.64 ), Z ), Y ) ) }.
% 1.30/1.64 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.30/1.64 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.30/1.64 ) ) = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X
% 1.30/1.64 , Y ) ) }.
% 1.30/1.64 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.30/1.64 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.30/1.64 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs(
% 1.30/1.64 X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.30/1.64 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 1.30/1.64 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.30/1.64 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 1.30/1.64 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 1.30/1.64 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.30/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ),
% 1.30/1.64 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Int_Oint, X, Y ) ) = c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 1.30/1.64 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ), c_Groups_Oabs__class_Oabs(
% 1.30/1.64 tc_Int_Oint, Y ) ) }.
% 1.30/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.30/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.30/1.64 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.30/1.64 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 1.30/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.30/1.64 ( tc_Int_Oint, Y ), X ) }.
% 1.30/1.64 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.30/1.64 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 1.30/1.64 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.64 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.30/1.64 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 1.30/1.64 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.30/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.30/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 1.30/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.30/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.30/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 1.30/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.30/1.64 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.30/1.64 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 1.30/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.30/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.30/1.64 }.
% 1.30/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.30/1.64 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.30/1.64 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.30/1.64 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.30/1.64 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.30/1.64 ) }.
% 1.30/1.64 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.30/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.30/1.64 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 1.30/1.64 }.
% 1.30/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z ), Y
% 1.30/1.64 ) = c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.30/1.64 , Y ) ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.30/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 1.30/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Int_Oint, X, Y ), X ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 1.30/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Int_Oint, Z, Y ), X ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.30/1.64 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.30/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.30/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.30/1.64 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 1.30/1.64 tc_Int_Oint, X ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 1.30/1.64 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 1.30/1.64 tc_Int_Oint, X ) = X }.
% 1.30/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.30/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 1.30/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.30/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.30/1.64 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 1.30/1.64 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.30/1.64 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.30/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.30/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.30/1.64 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.30/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 1.30/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.30/1.64 ( tc_Int_Oint, X, Y ) ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.30/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.30/1.64 ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.30/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.30/1.64 ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 1.30/1.64 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.30/1.64 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 1.30/1.64 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.30/1.64 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 1.30/1.64 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 1.30/1.64 ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 1.30/1.64 ( X, Z, Y ) = T }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 1.30/1.64 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 1.30/1.64 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 1.30/1.64 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 1.30/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 1.30/1.64 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 1.30/1.64 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.30/1.64 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 1.30/1.64 ), Y ) ) = Z }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.30/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 1.30/1.64 , Z ) ) = Y }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.30/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 1.30/1.64 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.30/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.30/1.64 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.30/1.64 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.30/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.30/1.64 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 1.30/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.30/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ),
% 1.30/1.64 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 1.30/1.64 tc_Int_Oint ) }.
% 1.30/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.30/1.64 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 1.30/1.64 tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 1.30/1.64 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.30/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.64 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.30/1.64 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 1.30/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.64 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.30/1.64 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 1.30/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 1.30/1.64 ) ) }.
% 1.30/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.30/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.30/1.64 ( tc_Int_Oint, Y, X ) ) }.
% 1.30/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.30/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 1.30/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.30/1.64 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.30/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 1.30/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.30/1.64 ( tc_Int_Oint, Y, X ) ) }.
% 1.30/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 1.30/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 1.30/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.30/1.64 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.30/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 1.30/1.64 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 1.30/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 1.30/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.64 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 1.30/1.64 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 1.30/1.64 ( X, Z, Y ), T ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.64 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 1.30/1.64 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 1.30/1.64 ( X, Z, Y ) ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.64 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.30/1.64 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 1.30/1.64 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.30/1.64 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 1.30/1.64 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.30/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.30/1.64 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.30/1.64 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.30/1.64 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 1.30/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.30/1.64 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 1.30/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.30/1.64 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.30/1.64 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.30/1.64 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 1.30/1.64 ( X ) ) ) }.
% 1.30/1.64 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.30/1.64 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.30/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.30/1.64 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.30/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Z, Y,
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.64 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.30/1.64 .
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.30/1.64 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.30/1.64 .
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.64 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.30/1.64 .
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.64 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 1.30/1.64 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 1.30/1.64 .
% 1.30/1.64 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.64 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.30/1.64 ( X ), T, Z ), Y ) }.
% 1.30/1.64 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 1.30/1.64 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 1.30/1.64 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.30/1.64 ( X ), Z, Y ) ) }.
% 1.30/1.64 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 1.30/1.64 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.30/1.64 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.30/1.64 ( X ), Z, Y ) ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.30/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.30/1.64 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 1.30/1.64 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 1.30/1.64 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.30/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.64 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.30/1.64 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 1.30/1.64 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Nat_Onat, Z, Y ), X ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 1.30/1.64 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 1.30/1.64 .
% 1.30/1.64 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.30/1.64 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.30/1.64 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 1.30/1.64 .
% 1.30/1.64 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.30/1.64 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.30/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 1.30/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 1.30/1.64 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 1.30/1.64 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.30/1.64 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.64 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.30/1.64 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 1.30/1.64 }.
% 1.30/1.64 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.64 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.30/1.64 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 1.30/1.64 ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.30/1.64 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.30/1.64 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 }.
% 1.30/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.30/1.64 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.64 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.30/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.30/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.30/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.30/1.64 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.30/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Nat_Onat, Y, X ), Y ) }.
% 1.30/1.64 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.30/1.64 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 1.30/1.64 ) ) }.
% 1.30/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), X ) =
% 1.30/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Divides_Odiv__class_Omod
% 1.30/1.64 ( tc_Nat_Onat, Y, X ) ) }.
% 1.30/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Y ) ) =
% 1.30/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Divides_Odiv__class_Omod
% 1.30/1.64 ( tc_Nat_Onat, X, Y ) ) }.
% 1.30/1.64 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.30/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv
% 1.30/1.64 ( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.30/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T,
% 1.30/1.64 c_Polynomial_Osmult( X, Y, Z ) ) = c_Polynomial_Osmult( X,
% 1.30/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Polynomial_Opoly( X ), T, Z ) ) }.
% 1.30/1.64 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.30/1.64 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.64 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 1.30/1.64 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.30/1.64 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.64 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 1.30/1.64 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.64 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.30/1.64 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.64 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.30/1.64 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.64 tc_Polynomial_Opoly( X ) ), Z ), c_Divides_Odiv__class_Omod(
% 1.30/1.64 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.30/1.64 ( X ), T, Z ), Y ) ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X
% 1.30/1.64 ), T, Z ) ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.30/1.64 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.30/1.64 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.30/1.64 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.30/1.64 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.30/1.64 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.30/1.64 alpha20( X, Z ) }.
% 1.30/1.64 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.30/1.64 alpha38( X, Y, Z ) }.
% 1.30/1.64 { ! alpha20( X, Z ), ! alpha38( X, Y, Z ), hBOOL( hAPP( Z,
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 1.30/1.64 { ! alpha38( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.64 alpha46( X, Y, Z ) }.
% 1.30/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha38( X, Y, Z ) }.
% 1.30/1.64 { ! alpha46( X, Y, Z ), alpha38( X, Y, Z ) }.
% 1.30/1.64 { ! alpha46( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.30/1.64 ), alpha50( X, Y, Z, T ) }.
% 1.30/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol18( X, T, U ), X ),
% 1.30/1.64 alpha46( X, Y, Z ) }.
% 1.30/1.64 { ! alpha50( X, Y, Z, skol18( X, Y, Z ) ), alpha46( X, Y, Z ) }.
% 1.30/1.64 { ! alpha50( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.30/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.30/1.64 hBOOL( hAPP( Z, U ) ) }.
% 1.30/1.64 { ! hBOOL( hAPP( Z, skol19( U, W, Z, V0 ) ) ), alpha50( X, Y, Z, T ) }.
% 1.30/1.64 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol19( X, Y, Z, T ) )
% 1.30/1.64 , T ), alpha50( X, Y, Z, T ) }.
% 1.30/1.64 { ! alpha20( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.64 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.30/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha20( X, Y ) }.
% 1.30/1.64 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha20
% 1.30/1.64 ( X, Y ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.64 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.30/1.64 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 1.30/1.64 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.30/1.64 tc_Polynomial_Opoly( X ), Y ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless(
% 1.30/1.64 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.30/1.64 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 1.30/1.64 tc_Polynomial_Opoly( X ), Y ) = Y }.
% 1.30/1.64 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.30/1.64 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc(
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.30/1.64 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X ) ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 1.30/1.64 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 1.30/1.64 }.
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.30/1.64 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.30/1.64 .
% 1.30/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 1.30/1.64 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 1.30/1.64 }.
% 1.30/1.64 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.64 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.64 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.64 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.64 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.64 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.30/1.64 c_Groups_Oone__class_Oone( X ) ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 1.30/1.64 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 1.30/1.64 ) ), ! alpha21( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Int_Oint ), X ), alpha21( X, Y, skol20( X, Y, Z ), skol26( X, Y, Z )
% 1.30/1.64 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 1.30/1.64 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.64 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol20( X, Y, Z ) ), skol26
% 1.30/1.64 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 1.30/1.64 ) }.
% 1.30/1.64 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 1.30/1.64 { ! alpha21( X, Y, Z, T ), alpha39( X, Y, Z, T ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha39( X, Y, Z, T )
% 1.30/1.64 , alpha21( X, Y, Z, T ) }.
% 1.30/1.64 { ! alpha39( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.30/1.64 ) }.
% 1.30/1.64 { ! alpha39( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.30/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.30/1.64 .
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha39( X,
% 1.30/1.64 Y, Z, T ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha22( X, Y, T,
% 1.30/1.64 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha22( X, Y, skol21( X, Y
% 1.30/1.64 , Z ), skol27( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.30/1.64 skol21( X, Y, Z ) ), skol27( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 1.30/1.64 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.30/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.30/1.64 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 1.30/1.64 ) }.
% 1.30/1.64 { ! alpha22( X, Y, Z, T ), alpha40( X, Y, Z, T ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha40( X, Y, Z
% 1.30/1.64 , T ), alpha22( X, Y, Z, T ) }.
% 1.30/1.64 { ! alpha40( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.64 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.30/1.64 { ! alpha40( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.30/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.30/1.64 .
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.30/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha40( X,
% 1.30/1.64 Y, Z, T ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.64 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 1.30/1.64 ) ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.30/1.64 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.30/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 1.30/1.64 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.30/1.64 ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.30/1.64 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.30/1.64 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.30/1.64 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.30/1.64 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.30/1.64 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.30/1.64 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.30/1.64 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 1.30/1.64 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 1.30/1.64 ) }.
% 1.30/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.30/1.64 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 1.30/1.64 ) }.
% 1.30/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.64 tc_Int_Oint, X, Y ) ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.64 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.64 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.30/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.30/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.30/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.64 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.30/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.30/1.65 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.30/1.65 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.65 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.65 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.30/1.65 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.30/1.65 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.30/1.65 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.65 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.65 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.65 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.30/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.65 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.65 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.65 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.30/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.65 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.30/1.65 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.30/1.65 ) ) }.
% 1.30/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.65 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.30/1.65 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.30/1.65 ) ) }.
% 1.30/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.65 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.30/1.65 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.30/1.65 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.65 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.30/1.65 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.30/1.65 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.30/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.30/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.65 }.
% 1.30/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.30/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.30/1.65 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.65 }.
% 1.30/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.30/1.65 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.65 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.30/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.30/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.30/1.65 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.30/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.30/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.30/1.65 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.30/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.30/1.65 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.65 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.30/1.65 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.30/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.65 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.65 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.30/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.30/1.65 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.30/1.65 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.30/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.65 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.30/1.65 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.30/1.65 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ),
% 1.30/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 1.30/1.65 ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__ab__semigroup__add( X ) }
% 1.30/1.65 .
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors( X ) }
% 1.30/1.65 .
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__semigroup__add( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__mult( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__mult( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__add( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__add( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__1( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__0( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Groups_Oab__group__add( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Ozero__neq__one( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__mult( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring__1( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__add( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Osemiring__0( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Groups_Ogroup__add( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Omult__zero( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Osemiring( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring__1( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Power_Opower( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Groups_Ozero( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Groups_Oone( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Odvd( X ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__comm__monoid__add( X ) }
% 1.30/1.65 .
% 1.30/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.30/1.65 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.30/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.30/1.65 tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.30/1.65 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.30/1.65 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.30/1.65 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.30/1.65 { class_Power_Opower( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.30/1.65 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.30/1.65 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.30/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.30/1.65 tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.30/1.65 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ),
% 1.30/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.30/1.65 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.30/1.65 ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.30/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.30/1.65 X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.30/1.65 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.30/1.65 ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.30/1.65 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.30/1.65 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 1.30/1.65 .
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.30/1.65 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.30/1.65 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.30/1.65 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.30/1.65 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.30/1.65 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.30/1.65 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.30/1.65 ( tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.30/1.65 ( tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.30/1.65 ( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Olinordered__idom( X ), class_Groups_Oabs__if(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.30/1.65 }.
% 1.30/1.65 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.30/1.65 ) ) }.
% 1.30/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.30/1.65 .
% 1.30/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.30/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.65 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.30/1.65 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.30/1.65 { ! hBOOL( c_fFalse ) }.
% 1.30/1.65 { hBOOL( c_fTrue ) }.
% 1.30/1.65 { X = c_Groups_Ozero__class_Ozero( t_a ), alpha55( Y, Z ), !
% 1.30/1.65 c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) =
% 1.30/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ), ! hAPP(
% 1.30/1.65 c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) )
% 1.30/1.65 , skol22( X, Y, Z ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( t_a )
% 1.30/1.65 , hAPP( hAPP( c_Power_Opower__class_Opower( t_a ), skol22( X, Y, Z ) ), Y
% 1.30/1.65 ) ), hAPP( c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, X, Z ) ),
% 1.30/1.65 skol22( X, Y, Z ) ) ) }.
% 1.30/1.65 { X = c_Groups_Ozero__class_Ozero( t_a ), alpha55( Y, Z ), ! c_Nat_OSuc(
% 1.30/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If( tc_Nat_Onat, c_fequal( Z
% 1.30/1.65 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) ),
% 1.30/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Nat_OSuc(
% 1.30/1.65 c_Polynomial_Odegree( t_a, Z ) ) ), Y ) ) = c_Nat_OSuc(
% 1.30/1.65 c_Polynomial_Odegree( t_a, c_Polynomial_OpCons( t_a, v_c____, v_cs____ )
% 1.30/1.65 ) ), ! hAPP( c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, v_c____
% 1.30/1.65 , v_cs____ ) ), skol22( X, Y, Z ) ) = hAPP( hAPP(
% 1.30/1.65 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.30/1.65 c_Power_Opower__class_Opower( t_a ), skol22( X, Y, Z ) ), Y ) ), hAPP(
% 1.30/1.65 c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, X, Z ) ), skol22( X, Y
% 1.30/1.65 , Z ) ) ) }.
% 1.30/1.65 { ! alpha55( X, Y ), c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) =
% 1.30/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) }.
% 1.30/1.65 { ! alpha55( X, Y ), ! c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.30/1.65 , c_If( tc_Nat_Onat, c_fequal( Y, c_Groups_Ozero__class_Ozero(
% 1.30/1.65 tc_Polynomial_Opoly( t_a ) ) ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.30/1.65 ), c_Nat_OSuc( c_Polynomial_Odegree( t_a, Y ) ) ), X ) ) =
% 1.30/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.65 { ! c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) =
% 1.30/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ), c_Nat_OSuc(
% 1.30/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If( tc_Nat_Onat, c_fequal( Y
% 1.30/1.65 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) ),
% 1.30/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Nat_OSuc(
% 1.30/1.65 c_Polynomial_Odegree( t_a, Y ) ) ), X ) ) = c_Groups_Ozero__class_Ozero(
% 1.30/1.65 tc_Nat_Onat ), alpha55( X, Y ) }.
% 1.30/1.65 { class_Rings_Oidom( t_a ) }.
% 1.30/1.65
% 1.30/1.65 *** allocated 15000 integers for clauses
% 1.30/1.65 *** allocated 22500 integers for clauses
% 1.30/1.65 *** allocated 33750 integers for clauses
% 1.30/1.65 *** allocated 50625 integers for clauses
% 1.30/1.65 *** allocated 75937 integers for clauses
% 1.30/1.65 *** allocated 113905 integers for clauses
% 1.30/1.65 percentage equality = 0.343783, percentage horn = 0.868024
% 1.30/1.65 This is a problem with some equality
% 1.30/1.65
% 1.30/1.65
% 1.30/1.65
% 1.30/1.65 Options Used:
% 1.30/1.65
% 1.30/1.65 useres = 1
% 1.30/1.65 useparamod = 1
% 1.30/1.65 useeqrefl = 1
% 1.30/1.65 useeqfact = 1
% 1.30/1.65 usefactor = 1
% 1.30/1.65 usesimpsplitting = 0
% 1.30/1.65 usesimpdemod = 5
% 1.30/1.65 usesimpres = 3
% 1.30/1.65
% 1.30/1.65 resimpinuse = 1000
% 1.30/1.65 resimpclauses = 20000
% 1.30/1.65 substype = eqrewr
% 1.30/1.65 backwardsubs = 1
% 1.30/1.65 selectoldest = 5
% 1.30/1.65
% 1.30/1.65 litorderings [0] = split
% 1.30/1.65 litorderings [1] = extend the termordering, first sorting on arguments
% 1.30/1.65
% 1.30/1.65 termordering = kbo
% 1.30/1.65
% 1.30/1.65 litapriori = 0
% 1.30/1.65 termapriori = 1
% 1.30/1.65 litaposteriori = 0
% 1.30/1.65 termaposteriori = 0
% 1.30/1.65 demodaposteriori = 0
% 1.30/1.65 ordereqreflfact = 0
% 1.30/1.65
% 1.30/1.65 litselect = negord
% 1.30/1.65
% 1.30/1.65 maxweight = 15
% 1.30/1.65 maxdepth = 30000
% 1.30/1.65 maxlength = 115
% 1.30/1.65 maxnrvars = 195
% 1.30/1.65 excuselevel = 1
% 1.30/1.65 increasemaxweight = 1
% 1.30/1.65
% 1.30/1.65 maxselected = 10000000
% 1.30/1.65 maxnrclauses = 10000000
% 1.30/1.65
% 1.30/1.65 showgenerated = 0
% 1.30/1.65 showkept = 0
% 1.30/1.65 showselected = 0
% 1.30/1.65 showdeleted = 0
% 1.30/1.65 showresimp = 1
% 1.30/1.65 showstatus = 2000
% 1.30/1.65
% 1.30/1.65 prologoutput = 0
% 1.30/1.65 nrgoals = 5000000
% 1.30/1.65 totalproof = 1
% 1.30/1.65
% 1.30/1.65 Symbols occurring in the translation:
% 1.30/1.65
% 1.30/1.65 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.30/1.65 . [1, 2] (w:1, o:186, a:1, s:1, b:0),
% 1.30/1.65 ! [4, 1] (w:0, o:109, a:1, s:1, b:0),
% 1.30/1.65 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.30/1.65 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.30/1.65 hAPP [38, 2] (w:1, o:210, a:1, s:1, b:0),
% 1.30/1.65 t_a [39, 0] (w:1, o:20, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Oidom [40, 1] (w:1, o:114, a:1, s:1, b:0),
% 1.30/1.65 v_c____ [41, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.30/1.65 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:115, a:1, s:1, b:0),
% 1.30/1.65 v_cs____ [44, 0] (w:1, o:23, a:1, s:1, b:0),
% 1.30/1.65 c_Polynomial_OpCons [45, 3] (w:1, o:239, a:1, s:1, b:0),
% 1.30/1.65 c_Polynomial_Opoly [46, 2] (w:1, o:211, a:1, s:1, b:0),
% 1.30/1.65 v_p [47, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.30/1.65 class_Groups_Ozero [51, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.30/1.65 tc_Polynomial_Opoly [52, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.30/1.65 c_Polynomial_Odegree [53, 2] (w:1, o:213, a:1, s:1, b:0),
% 1.30/1.65 tc_Nat_Onat [54, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.30/1.65 c_Nat_OSuc [55, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Ocomm__semiring__0 [57, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.30/1.65 c_Groups_Otimes__class_Otimes [58, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.30/1.65 c_Groups_Oplus__class_Oplus [59, 3] (w:1, o:241, a:1, s:1, b:0),
% 1.30/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [60, 2] (w:1, o:214
% 1.30/1.65 , a:1, s:1, b:0),
% 1.30/1.65 c_fequal [64, 2] (w:1, o:215, a:1, s:1, b:0),
% 1.30/1.65 c_If [65, 4] (w:1, o:291, a:1, s:1, b:0),
% 1.30/1.65 c_Power_Opower__class_Opower [66, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.30/1.65 class_Groups_Ocomm__monoid__add [76, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.30/1.65
% 1.30/1.65 class_Int_Oring__char__0 [84, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Ocomm__semiring__1 [88, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.30/1.65 class_Groups_Omonoid__mult [89, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.30/1.65 class_Power_Opower [90, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Osemiring__0 [91, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Omult__zero [92, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Ono__zero__divisors [93, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.30/1.65
% 1.30/1.65 class_Rings_Ozero__neq__one [94, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.30/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [98
% 1.30/1.65 , 1] (w:1, o:162, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Olinordered__ring__strict [101, 1] (w:1, o:140, a:1, s:1
% 1.30/1.65 , b:0),
% 1.30/1.65 class_Rings_Oring__1__no__zero__divisors [110, 1] (w:1, o:135, a:1
% 1.30/1.65 , s:1, b:0),
% 1.30/1.65 class_Groups_Ocomm__monoid__mult [111, 1] (w:1, o:163, a:1, s:1, b:0)
% 1.30/1.65 ,
% 1.30/1.65 c_Polynomial_Opcompose [112, 3] (w:1, o:242, a:1, s:1, b:0),
% 1.30/1.65 c_Polynomial_Oorder [113, 3] (w:1, o:238, a:1, s:1, b:0),
% 1.30/1.65 class_RealVector_Oreal__normed__algebra [118, 1] (w:1, o:150, a:1, s:
% 1.30/1.65 1, b:0),
% 1.30/1.65 class_Rings_Ocomm__semiring [120, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Osemiring [124, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Oring__no__zero__divisors [125, 1] (w:1, o:136, a:1, s:1
% 1.30/1.65 , b:0),
% 1.30/1.65 class_Groups_Olinordered__ab__group__add [126, 1] (w:1, o:132, a:1
% 1.30/1.65 , s:1, b:0),
% 1.30/1.65 class_Groups_Omonoid__add [127, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.30/1.65 c_Polynomial_Opoly__rec [129, 5] (w:1, o:319, a:1, s:1, b:0),
% 1.30/1.65 c_Polynomial_Osynthetic__div [130, 3] (w:1, o:243, a:1, s:1, b:0),
% 1.30/1.65 c_Groups_Oone__class_Oone [131, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.30/1.65 class_Groups_Oone [132, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.30/1.65 class_Groups_Oab__semigroup__mult [133, 1] (w:1, o:167, a:1, s:1, b:0
% 1.30/1.65 ),
% 1.30/1.65 class_Groups_Oab__semigroup__add [134, 1] (w:1, o:168, a:1, s:1, b:0)
% 1.30/1.65 ,
% 1.30/1.65 class_Groups_Ocancel__semigroup__add [135, 1] (w:1, o:169, a:1, s:1
% 1.30/1.65 , b:0),
% 1.30/1.65 class_Groups_Ocancel__ab__semigroup__add [136, 1] (w:1, o:170, a:1
% 1.30/1.65 , s:1, b:0),
% 1.30/1.65 tc_Int_Oint [137, 0] (w:1, o:94, a:1, s:1, b:0),
% 1.30/1.65 c_Power_Opower_Opower [138, 3] (w:1, o:244, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Ocomm__ring__1 [139, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.30/1.65 c_Groups_Ouminus__class_Ouminus [140, 2] (w:1, o:216, a:1, s:1, b:0)
% 1.30/1.65 ,
% 1.30/1.65 c_Polynomial_Omonom [141, 3] (w:1, o:245, a:1, s:1, b:0),
% 1.30/1.65 c_Polynomial_Osmult [142, 3] (w:1, o:246, a:1, s:1, b:0),
% 1.30/1.65 c_Nat_Onat_Onat__size [144, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.30/1.65 c_Polynomial_Ocoeff [145, 2] (w:1, o:212, a:1, s:1, b:0),
% 1.30/1.65 class_Groups_Ogroup__add [146, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Ocomm__ring [151, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.30/1.65 class_Groups_Oab__group__add [152, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Oring [154, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Oring__1 [155, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.30/1.65 c_Nat_Osize__class_Osize [158, 2] (w:1, o:217, a:1, s:1, b:0),
% 1.30/1.65 c_Rings_Odvd__class_Odvd [159, 3] (w:1, o:247, a:1, s:1, b:0),
% 1.30/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [161, 3] (w:
% 1.30/1.65 1, o:240, a:1, s:1, b:0),
% 1.30/1.65 class_Fields_Ofield [162, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.30/1.65 c_Polynomial_Opoly__gcd [163, 3] (w:1, o:248, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Odvd [164, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.30/1.65 hBOOL [168, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.30/1.65 c_Rings_Oinverse__class_Oinverse [169, 2] (w:1, o:218, a:1, s:1, b:0)
% 1.30/1.65 ,
% 1.30/1.65 c_fTrue [170, 0] (w:1, o:102, a:1, s:1, b:0),
% 1.30/1.65 c_HOL_Obool_Obool__size [171, 1] (w:1, o:175, a:1, s:1, b:0),
% 1.30/1.65 c_fFalse [172, 0] (w:1, o:103, a:1, s:1, b:0),
% 1.30/1.65 c_Groups_Ominus__class_Ominus [173, 3] (w:1, o:249, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Odivision__ring [175, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Odivision__ring__inverse__zero [176, 1] (w:1, o:155, a:1
% 1.30/1.65 , s:1, b:0),
% 1.30/1.65 class_Fields_Ofield__inverse__zero [179, 1] (w:1, o:117, a:1, s:1, b:
% 1.30/1.65 0),
% 1.30/1.65 c_Divides_Odiv__class_Omod [180, 3] (w:1, o:250, a:1, s:1, b:0),
% 1.30/1.65 c_Orderings_Oord__class_Oless [181, 3] (w:1, o:236, a:1, s:1, b:0),
% 1.30/1.65 class_RealVector_Oreal__normed__field [182, 1] (w:1, o:156, a:1, s:1
% 1.30/1.65 , b:0),
% 1.30/1.65 c_Rings_Oinverse__class_Odivide [183, 3] (w:1, o:251, a:1, s:1, b:0)
% 1.30/1.65 ,
% 1.30/1.65 class_Fields_Olinordered__field [185, 1] (w:1, o:118, a:1, s:1, b:0)
% 1.30/1.65 ,
% 1.30/1.65 class_Fields_Olinordered__field__inverse__zero [186, 1] (w:1, o:119
% 1.30/1.65 , a:1, s:1, b:0),
% 1.30/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le [187, 1] (w:1, o:
% 1.30/1.65 176, a:1, s:1, b:0),
% 1.30/1.65 class_Groups_Oordered__cancel__ab__semigroup__add [188, 1] (w:1, o:
% 1.30/1.65 177, a:1, s:1, b:0),
% 1.30/1.65 class_Groups_Oordered__ab__group__add [189, 1] (w:1, o:178, a:1, s:1
% 1.30/1.65 , b:0),
% 1.30/1.65 class_Rings_Olinordered__idom [192, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Olinordered__semidom [194, 1] (w:1, o:143, a:1, s:1, b:0)
% 1.30/1.65 ,
% 1.30/1.65 class_Rings_Olinordered__comm__semiring__strict [195, 1] (w:1, o:144
% 1.30/1.65 , a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Olinordered__semiring__strict [196, 1] (w:1, o:145, a:1
% 1.30/1.65 , s:1, b:0),
% 1.30/1.65 class_Rings_Olinordered__ring [197, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.30/1.65 class_Groups_Oordered__comm__monoid__add [198, 1] (w:1, o:179, a:1
% 1.30/1.65 , s:1, b:0),
% 1.30/1.65 class_RealVector_Oreal__field [203, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.30/1.65 class_Rings_Oordered__ring [204, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.30/1.65 class_Divides_Osemiring__div [206, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.30/1.65 class_Divides_Oring__div [209, 1] (w:1, o:180, a:1, s:1, b:0),
% 1.30/1.65 c_Polynomial_Opdivmod__rel [210, 5] (w:1, o:320, a:1, s:1, b:0),
% 1.30/1.65 c_Polynomial_Opos__poly [218, 2] (w:1, o:219, a:1, s:1, b:0),
% 1.30/1.65 c_Divides_Odiv__class_Odiv [219, 3] (w:1, o:252, a:1, s:1, b:0),
% 1.30/1.65 c_Groups_Oabs__class_Oabs [220, 2] (w:1, o:220, a:1, s:1, b:0),
% 1.30/1.65 class_Groups_Oordered__ab__group__add__abs [221, 1] (w:1, o:182, a:1
% 1.30/1.65 , s:1, b:0),
% 1.30/1.65 class_Groups_Oabs__if [222, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.30/1.65 c_Groups_Osgn__class_Osgn [223, 2] (w:1, o:221, a:1, s:1, b:0),
% 6.29/6.67 class_RealVector_Oreal__normed__vector [224, 1] (w:1, o:159, a:1, s:1
% 6.29/6.67 , b:0),
% 6.29/6.67 class_RealVector_Oreal__normed__algebra__1 [225, 1] (w:1, o:160, a:1
% 6.29/6.67 , s:1, b:0),
% 6.29/6.67 class_RealVector_Oreal__normed__div__algebra [226, 1] (w:1, o:161, a:
% 6.29/6.67 1, s:1, b:0),
% 6.29/6.67 class_Groups_Osgn__if [227, 1] (w:1, o:184, a:1, s:1, b:0),
% 6.29/6.67 c_Orderings_Oord__class_Oless__eq [228, 3] (w:1, o:237, a:1, s:1, b:0
% 6.29/6.67 ),
% 6.29/6.67 class_Rings_Olinordered__semiring [229, 1] (w:1, o:146, a:1, s:1, b:0
% 6.29/6.67 ),
% 6.29/6.67 class_Groups_Ocancel__comm__monoid__add [231, 1] (w:1, o:185, a:1, s:
% 6.29/6.67 1, b:0),
% 6.29/6.67 alpha1 [233, 2] (w:1, o:222, a:1, s:1, b:1),
% 6.29/6.67 alpha2 [234, 2] (w:1, o:224, a:1, s:1, b:1),
% 6.29/6.67 alpha3 [235, 3] (w:1, o:255, a:1, s:1, b:1),
% 6.29/6.67 alpha4 [236, 2] (w:1, o:225, a:1, s:1, b:1),
% 6.29/6.67 alpha5 [237, 2] (w:1, o:226, a:1, s:1, b:1),
% 6.29/6.67 alpha6 [238, 3] (w:1, o:259, a:1, s:1, b:1),
% 6.29/6.67 alpha7 [239, 3] (w:1, o:260, a:1, s:1, b:1),
% 6.29/6.67 alpha8 [240, 3] (w:1, o:261, a:1, s:1, b:1),
% 6.29/6.67 alpha9 [241, 3] (w:1, o:262, a:1, s:1, b:1),
% 6.29/6.67 alpha10 [242, 3] (w:1, o:263, a:1, s:1, b:1),
% 6.29/6.67 alpha11 [243, 3] (w:1, o:264, a:1, s:1, b:1),
% 6.29/6.67 alpha12 [244, 4] (w:1, o:292, a:1, s:1, b:1),
% 6.29/6.67 alpha13 [245, 4] (w:1, o:293, a:1, s:1, b:1),
% 6.29/6.67 alpha14 [246, 2] (w:1, o:223, a:1, s:1, b:1),
% 6.29/6.67 alpha15 [247, 3] (w:1, o:265, a:1, s:1, b:1),
% 6.29/6.67 alpha16 [248, 3] (w:1, o:266, a:1, s:1, b:1),
% 6.29/6.67 alpha17 [249, 3] (w:1, o:267, a:1, s:1, b:1),
% 6.29/6.67 alpha18 [250, 3] (w:1, o:268, a:1, s:1, b:1),
% 6.29/6.67 alpha19 [251, 3] (w:1, o:269, a:1, s:1, b:1),
% 6.29/6.67 alpha20 [252, 2] (w:1, o:227, a:1, s:1, b:1),
% 6.29/6.67 alpha21 [253, 4] (w:1, o:294, a:1, s:1, b:1),
% 6.29/6.67 alpha22 [254, 4] (w:1, o:295, a:1, s:1, b:1),
% 6.29/6.67 alpha23 [255, 2] (w:1, o:228, a:1, s:1, b:1),
% 6.29/6.67 alpha24 [256, 2] (w:1, o:229, a:1, s:1, b:1),
% 6.29/6.67 alpha25 [257, 4] (w:1, o:296, a:1, s:1, b:1),
% 6.29/6.67 alpha26 [258, 3] (w:1, o:253, a:1, s:1, b:1),
% 6.29/6.67 alpha27 [259, 3] (w:1, o:254, a:1, s:1, b:1),
% 6.29/6.67 alpha28 [260, 4] (w:1, o:297, a:1, s:1, b:1),
% 6.29/6.67 alpha29 [261, 4] (w:1, o:298, a:1, s:1, b:1),
% 6.29/6.67 alpha30 [262, 4] (w:1, o:299, a:1, s:1, b:1),
% 6.29/6.67 alpha31 [263, 4] (w:1, o:300, a:1, s:1, b:1),
% 6.29/6.67 alpha32 [264, 4] (w:1, o:301, a:1, s:1, b:1),
% 6.29/6.67 alpha33 [265, 4] (w:1, o:302, a:1, s:1, b:1),
% 6.29/6.67 alpha34 [266, 3] (w:1, o:270, a:1, s:1, b:1),
% 6.29/6.67 alpha35 [267, 3] (w:1, o:271, a:1, s:1, b:1),
% 6.29/6.67 alpha36 [268, 3] (w:1, o:272, a:1, s:1, b:1),
% 6.29/6.67 alpha37 [269, 3] (w:1, o:273, a:1, s:1, b:1),
% 6.29/6.67 alpha38 [270, 3] (w:1, o:274, a:1, s:1, b:1),
% 6.29/6.67 alpha39 [271, 4] (w:1, o:303, a:1, s:1, b:1),
% 6.29/6.67 alpha40 [272, 4] (w:1, o:304, a:1, s:1, b:1),
% 6.29/6.67 alpha41 [273, 4] (w:1, o:305, a:1, s:1, b:1),
% 6.29/6.67 alpha42 [274, 4] (w:1, o:306, a:1, s:1, b:1),
% 6.29/6.67 alpha43 [275, 3] (w:1, o:275, a:1, s:1, b:1),
% 6.29/6.67 alpha44 [276, 4] (w:1, o:307, a:1, s:1, b:1),
% 6.29/6.67 alpha45 [277, 3] (w:1, o:276, a:1, s:1, b:1),
% 6.29/6.67 alpha46 [278, 3] (w:1, o:277, a:1, s:1, b:1),
% 6.29/6.67 alpha47 [279, 4] (w:1, o:308, a:1, s:1, b:1),
% 6.29/6.67 alpha48 [280, 4] (w:1, o:309, a:1, s:1, b:1),
% 6.29/6.67 alpha49 [281, 4] (w:1, o:310, a:1, s:1, b:1),
% 6.29/6.67 alpha50 [282, 4] (w:1, o:311, a:1, s:1, b:1),
% 6.29/6.67 alpha51 [283, 4] (w:1, o:312, a:1, s:1, b:1),
% 6.29/6.67 alpha52 [284, 4] (w:1, o:313, a:1, s:1, b:1),
% 6.29/6.67 alpha53 [285, 3] (w:1, o:256, a:1, s:1, b:1),
% 6.29/6.67 alpha54 [286, 3] (w:1, o:257, a:1, s:1, b:1),
% 6.29/6.67 alpha55 [287, 2] (w:1, o:230, a:1, s:1, b:1),
% 6.29/6.67 alpha56 [288, 4] (w:1, o:314, a:1, s:1, b:1),
% 6.29/6.67 alpha57 [289, 3] (w:1, o:258, a:1, s:1, b:1),
% 6.29/6.67 alpha58 [290, 4] (w:1, o:315, a:1, s:1, b:1),
% 6.29/6.67 alpha59 [291, 4] (w:1, o:316, a:1, s:1, b:1),
% 6.29/6.67 skol1 [292, 2] (w:1, o:231, a:1, s:1, b:1),
% 6.29/6.67 skol2 [293, 0] (w:1, o:12, a:1, s:1, b:1),
% 6.29/6.67 skol3 [294, 0] (w:1, o:17, a:1, s:1, b:1),
% 6.29/6.67 skol4 [295, 0] (w:1, o:18, a:1, s:1, b:1),
% 6.29/6.67 skol5 [296, 0] (w:1, o:19, a:1, s:1, b:1),
% 6.29/6.67 skol6 [297, 3] (w:1, o:278, a:1, s:1, b:1),
% 6.29/6.67 skol7 [298, 3] (w:1, o:279, a:1, s:1, b:1),
% 33.54/33.92 skol8 [299, 4] (w:1, o:317, a:1, s:1, b:1),
% 33.54/33.92 skol9 [300, 2] (w:1, o:232, a:1, s:1, b:1),
% 33.54/33.92 skol10 [301, 1] (w:1, o:121, a:1, s:1, b:1),
% 33.54/33.92 skol11 [302, 2] (w:1, o:233, a:1, s:1, b:1),
% 33.54/33.92 skol12 [303, 3] (w:1, o:280, a:1, s:1, b:1),
% 33.54/33.92 skol13 [304, 3] (w:1, o:281, a:1, s:1, b:1),
% 33.54/33.92 skol14 [305, 2] (w:1, o:234, a:1, s:1, b:1),
% 33.54/33.92 skol15 [306, 2] (w:1, o:235, a:1, s:1, b:1),
% 33.54/33.92 skol16 [307, 3] (w:1, o:282, a:1, s:1, b:1),
% 33.54/33.92 skol17 [308, 3] (w:1, o:283, a:1, s:1, b:1),
% 33.54/33.92 skol18 [309, 3] (w:1, o:284, a:1, s:1, b:1),
% 33.54/33.92 skol19 [310, 4] (w:1, o:318, a:1, s:1, b:1),
% 33.54/33.92 skol20 [311, 3] (w:1, o:285, a:1, s:1, b:1),
% 33.54/33.92 skol21 [312, 3] (w:1, o:286, a:1, s:1, b:1),
% 33.54/33.92 skol22 [313, 3] (w:1, o:287, a:1, s:1, b:1),
% 33.54/33.92 skol23 [314, 0] (w:1, o:13, a:1, s:1, b:1),
% 33.54/33.92 skol24 [315, 0] (w:1, o:14, a:1, s:1, b:1),
% 33.54/33.92 skol25 [316, 3] (w:1, o:288, a:1, s:1, b:1),
% 33.54/33.92 skol26 [317, 3] (w:1, o:289, a:1, s:1, b:1),
% 33.54/33.92 skol27 [318, 3] (w:1, o:290, a:1, s:1, b:1),
% 33.54/33.92 skol28 [319, 0] (w:1, o:15, a:1, s:1, b:1),
% 33.54/33.92 skol29 [320, 0] (w:1, o:16, a:1, s:1, b:1).
% 33.54/33.92
% 33.54/33.92
% 33.54/33.92 Starting Search:
% 33.54/33.92
% 33.54/33.92 *** allocated 170857 integers for clauses
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 *** allocated 256285 integers for clauses
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 3002
% 33.54/33.92 Kept: 2050
% 33.54/33.92 Inuse: 53
% 33.54/33.92 Deleted: 8
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 *** allocated 170857 integers for termspace/termends
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 *** allocated 384427 integers for clauses
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 10949
% 33.54/33.92 Kept: 4307
% 33.54/33.92 Inuse: 193
% 33.54/33.92 Deleted: 28
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 *** allocated 256285 integers for termspace/termends
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 19603
% 33.54/33.92 Kept: 6335
% 33.54/33.92 Inuse: 252
% 33.54/33.92 Deleted: 29
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 *** allocated 576640 integers for clauses
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 29676
% 33.54/33.92 Kept: 8335
% 33.54/33.92 Inuse: 298
% 33.54/33.92 Deleted: 32
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 *** allocated 384427 integers for termspace/termends
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 37966
% 33.54/33.92 Kept: 10353
% 33.54/33.92 Inuse: 332
% 33.54/33.92 Deleted: 32
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 *** allocated 864960 integers for clauses
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 47883
% 33.54/33.92 Kept: 12872
% 33.54/33.92 Inuse: 354
% 33.54/33.92 Deleted: 32
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 52951
% 33.54/33.92 Kept: 15180
% 33.54/33.92 Inuse: 374
% 33.54/33.92 Deleted: 32
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 57783
% 33.54/33.92 Kept: 17191
% 33.54/33.92 Inuse: 414
% 33.54/33.92 Deleted: 35
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 *** allocated 576640 integers for termspace/termends
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 *** allocated 1297440 integers for clauses
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 63800
% 33.54/33.92 Kept: 19326
% 33.54/33.92 Inuse: 449
% 33.54/33.92 Deleted: 37
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 Resimplifying clauses:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 85256
% 33.54/33.92 Kept: 22126
% 33.54/33.92 Inuse: 469
% 33.54/33.92 Deleted: 230
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 *** allocated 864960 integers for termspace/termends
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 93909
% 33.54/33.92 Kept: 24197
% 33.54/33.92 Inuse: 484
% 33.54/33.92 Deleted: 230
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 101115
% 33.54/33.92 Kept: 26238
% 33.54/33.92 Inuse: 515
% 33.54/33.92 Deleted: 230
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92 *** allocated 1946160 integers for clauses
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 112666
% 33.54/33.92 Kept: 28539
% 33.54/33.92 Inuse: 554
% 33.54/33.92 Deleted: 230
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 120205
% 33.54/33.92 Kept: 31087
% 33.54/33.92 Inuse: 579
% 33.54/33.92 Deleted: 230
% 33.54/33.92 Deletedinuse: 0
% 33.54/33.92
% 33.54/33.92 Resimplifying inuse:
% 33.54/33.92 Done
% 33.54/33.92
% 33.54/33.92
% 33.54/33.92 Intermediate Status:
% 33.54/33.92 Generated: 145440
% 33.54/33.92 Kept: 33590
% 33.54/33.92 Inuse: 594
% 101.61/102.02 Deleted: 230
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 *** allocated 1297440 integers for termspace/termends
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 157050
% 101.61/102.02 Kept: 36149
% 101.61/102.02 Inuse: 614
% 101.61/102.02 Deleted: 230
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 166493
% 101.61/102.02 Kept: 38312
% 101.61/102.02 Inuse: 634
% 101.61/102.02 Deleted: 230
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 175987
% 101.61/102.02 Kept: 40486
% 101.61/102.02 Inuse: 651
% 101.61/102.02 Deleted: 230
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying clauses:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 *** allocated 2919240 integers for clauses
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 195017
% 101.61/102.02 Kept: 43054
% 101.61/102.02 Inuse: 679
% 101.61/102.02 Deleted: 345
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 212543
% 101.61/102.02 Kept: 45141
% 101.61/102.02 Inuse: 699
% 101.61/102.02 Deleted: 345
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 219376
% 101.61/102.02 Kept: 47151
% 101.61/102.02 Inuse: 720
% 101.61/102.02 Deleted: 345
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 *** allocated 1946160 integers for termspace/termends
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 229622
% 101.61/102.02 Kept: 49268
% 101.61/102.02 Inuse: 769
% 101.61/102.02 Deleted: 345
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 237798
% 101.61/102.02 Kept: 51291
% 101.61/102.02 Inuse: 814
% 101.61/102.02 Deleted: 345
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 245522
% 101.61/102.02 Kept: 54173
% 101.61/102.02 Inuse: 829
% 101.61/102.02 Deleted: 345
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 250103
% 101.61/102.02 Kept: 56183
% 101.61/102.02 Inuse: 835
% 101.61/102.02 Deleted: 345
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 260720
% 101.61/102.02 Kept: 58389
% 101.61/102.02 Inuse: 863
% 101.61/102.02 Deleted: 346
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 280491
% 101.61/102.02 Kept: 60971
% 101.61/102.02 Inuse: 888
% 101.61/102.02 Deleted: 346
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying clauses:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 291779
% 101.61/102.02 Kept: 62978
% 101.61/102.02 Inuse: 913
% 101.61/102.02 Deleted: 500
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 *** allocated 4378860 integers for clauses
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 309532
% 101.61/102.02 Kept: 66164
% 101.61/102.02 Inuse: 928
% 101.61/102.02 Deleted: 500
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 321785
% 101.61/102.02 Kept: 68400
% 101.61/102.02 Inuse: 943
% 101.61/102.02 Deleted: 500
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 330669
% 101.61/102.02 Kept: 70459
% 101.61/102.02 Inuse: 963
% 101.61/102.02 Deleted: 500
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 *** allocated 2919240 integers for termspace/termends
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 338936
% 101.61/102.02 Kept: 72574
% 101.61/102.02 Inuse: 978
% 101.61/102.02 Deleted: 500
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 351273
% 101.61/102.02 Kept: 75269
% 101.61/102.02 Inuse: 993
% 101.61/102.02 Deleted: 500
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 368285
% 101.61/102.02 Kept: 78994
% 101.61/102.02 Inuse: 1018
% 101.61/102.02 Deleted: 500
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 377720
% 101.61/102.02 Kept: 81817
% 101.61/102.02 Inuse: 1028
% 101.61/102.02 Deleted: 500
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying clauses:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 389637
% 101.61/102.02 Kept: 84013
% 101.61/102.02 Inuse: 1058
% 101.61/102.02 Deleted: 556
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 404372
% 101.61/102.02 Kept: 86739
% 101.61/102.02 Inuse: 1078
% 101.61/102.02 Deleted: 556
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02
% 101.61/102.02 Intermediate Status:
% 101.61/102.02 Generated: 416680
% 101.61/102.02 Kept: 89667
% 101.61/102.02 Inuse: 1088
% 101.61/102.02 Deleted: 556
% 101.61/102.02 Deletedinuse: 0
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 101.61/102.02
% 101.61/102.02 Resimplifying inuse:
% 101.61/102.02 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 435727
% 202.30/202.78 Kept: 93206
% 202.30/202.78 Inuse: 1118
% 202.30/202.78 Deleted: 556
% 202.30/202.78 Deletedinuse: 0
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 *** allocated 6568290 integers for clauses
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 451067
% 202.30/202.78 Kept: 96237
% 202.30/202.78 Inuse: 1138
% 202.30/202.78 Deleted: 556
% 202.30/202.78 Deletedinuse: 0
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 461772
% 202.30/202.78 Kept: 100170
% 202.30/202.78 Inuse: 1158
% 202.30/202.78 Deleted: 556
% 202.30/202.78 Deletedinuse: 0
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 469546
% 202.30/202.78 Kept: 103426
% 202.30/202.78 Inuse: 1168
% 202.30/202.78 Deleted: 556
% 202.30/202.78 Deletedinuse: 0
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying clauses:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 *** allocated 4378860 integers for termspace/termends
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 497936
% 202.30/202.78 Kept: 106998
% 202.30/202.78 Inuse: 1178
% 202.30/202.78 Deleted: 642
% 202.30/202.78 Deletedinuse: 0
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 508026
% 202.30/202.78 Kept: 109031
% 202.30/202.78 Inuse: 1198
% 202.30/202.78 Deleted: 642
% 202.30/202.78 Deletedinuse: 0
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 523271
% 202.30/202.78 Kept: 111184
% 202.30/202.78 Inuse: 1224
% 202.30/202.78 Deleted: 662
% 202.30/202.78 Deletedinuse: 1
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 530976
% 202.30/202.78 Kept: 113527
% 202.30/202.78 Inuse: 1229
% 202.30/202.78 Deleted: 682
% 202.30/202.78 Deletedinuse: 1
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 544220
% 202.30/202.78 Kept: 115818
% 202.30/202.78 Inuse: 1237
% 202.30/202.78 Deleted: 694
% 202.30/202.78 Deletedinuse: 1
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 560147
% 202.30/202.78 Kept: 118476
% 202.30/202.78 Inuse: 1239
% 202.30/202.78 Deleted: 703
% 202.30/202.78 Deletedinuse: 2
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 585119
% 202.30/202.78 Kept: 121507
% 202.30/202.78 Inuse: 1242
% 202.30/202.78 Deleted: 715
% 202.30/202.78 Deletedinuse: 2
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 593387
% 202.30/202.78 Kept: 123687
% 202.30/202.78 Inuse: 1255
% 202.30/202.78 Deleted: 742
% 202.30/202.78 Deletedinuse: 2
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying clauses:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 601903
% 202.30/202.78 Kept: 125707
% 202.30/202.78 Inuse: 1265
% 202.30/202.78 Deleted: 1299
% 202.30/202.78 Deletedinuse: 2
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 609056
% 202.30/202.78 Kept: 128107
% 202.30/202.78 Inuse: 1275
% 202.30/202.78 Deleted: 1299
% 202.30/202.78 Deletedinuse: 2
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 619190
% 202.30/202.78 Kept: 130682
% 202.30/202.78 Inuse: 1290
% 202.30/202.78 Deleted: 1299
% 202.30/202.78 Deletedinuse: 2
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 627194
% 202.30/202.78 Kept: 132691
% 202.30/202.78 Inuse: 1307
% 202.30/202.78 Deleted: 1299
% 202.30/202.78 Deletedinuse: 2
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 642548
% 202.30/202.78 Kept: 135673
% 202.30/202.78 Inuse: 1315
% 202.30/202.78 Deleted: 1299
% 202.30/202.78 Deletedinuse: 2
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 653199
% 202.30/202.78 Kept: 138358
% 202.30/202.78 Inuse: 1330
% 202.30/202.78 Deleted: 1299
% 202.30/202.78 Deletedinuse: 2
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 662361
% 202.30/202.78 Kept: 140418
% 202.30/202.78 Inuse: 1340
% 202.30/202.78 Deleted: 1299
% 202.30/202.78 Deletedinuse: 2
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 *** allocated 9852435 integers for clauses
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 691179
% 202.30/202.78 Kept: 142498
% 202.30/202.78 Inuse: 1380
% 202.30/202.78 Deleted: 1301
% 202.30/202.78 Deletedinuse: 4
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 700867
% 202.30/202.78 Kept: 144553
% 202.30/202.78 Inuse: 1390
% 202.30/202.78 Deleted: 1301
% 202.30/202.78 Deletedinuse: 4
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying clauses:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 711151
% 202.30/202.78 Kept: 146559
% 202.30/202.78 Inuse: 1400
% 202.30/202.78 Deleted: 2263
% 202.30/202.78 Deletedinuse: 4
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 721030
% 202.30/202.78 Kept: 148601
% 202.30/202.78 Inuse: 1430
% 202.30/202.78 Deleted: 2263
% 202.30/202.78 Deletedinuse: 4
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 Generated: 731618
% 202.30/202.78 Kept: 150633
% 202.30/202.78 Inuse: 1468
% 202.30/202.78 Deleted: 2263
% 202.30/202.78 Deletedinuse: 4
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 Resimplifying inuse:
% 202.30/202.78 Done
% 202.30/202.78
% 202.30/202.78 *** allocated 6568290 integers for termspace/termends
% 202.30/202.78
% 202.30/202.78 Intermediate Status:
% 202.30/202.78 GeCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------