TSTP Solution File: SWW188+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW188+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.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 23:21:08 EDT 2022
% Result : Timeout 300.02s 300.48s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW188+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Jun 4 23:26:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.34/1.73 *** allocated 10000 integers for termspace/termends
% 1.34/1.73 *** allocated 10000 integers for clauses
% 1.34/1.73 *** allocated 10000 integers for justifications
% 1.34/1.73 *** allocated 15000 integers for termspace/termends
% 1.34/1.73 *** allocated 22500 integers for termspace/termends
% 1.34/1.73 *** allocated 33750 integers for termspace/termends
% 1.34/1.73 Bliksem 1.12
% 1.34/1.73
% 1.34/1.73
% 1.34/1.73 Automatic Strategy Selection
% 1.34/1.73
% 1.34/1.73 *** allocated 50625 integers for termspace/termends
% 1.34/1.73 *** allocated 75937 integers for termspace/termends
% 1.34/1.73 *** allocated 113905 integers for termspace/termends
% 1.34/1.73
% 1.34/1.73 Clauses:
% 1.34/1.73
% 1.34/1.73 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.34/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.34/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.34/1.73 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), !
% 1.34/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.34/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.34/1.73 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 1.34/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 1.34/1.73 c_Polynomial_OpCons( X, T,
% 1.34/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.34/1.73 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.34/1.73 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 1.34/1.73 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.34/1.73 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.34/1.73 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.34/1.73 c_Polynomial_Odegree( X, Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 1.34/1.73 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 1.34/1.73 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.34/1.73 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.34/1.73 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.34/1.73 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.34/1.73 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.34/1.73 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.34/1.73 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha1( X, Y ), alpha24
% 1.34/1.73 ( X, Y ) }.
% 1.34/1.73 { ! alpha1( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.34/1.73 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! alpha24( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.34/1.73 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! alpha24( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! alpha24( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha24( X, Y ) }.
% 1.34/1.73 { ! alpha1( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! alpha1( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha2( X, Y ), alpha25( X
% 1.34/1.73 , Y ) }.
% 1.34/1.73 { ! alpha2( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.34/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! alpha25( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.34/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! alpha25( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! alpha25( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha25( X, Y ) }.
% 1.34/1.73 { ! alpha2( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 1.34/1.73 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.34/1.73 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.34/1.73 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.34/1.73 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.34/1.73 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.34/1.73 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.34/1.73 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.34/1.73 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.34/1.73 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.34/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 T, Y ), Z = Y }.
% 1.34/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 T, Y ) }.
% 1.34/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Y, Z ), T = Y }.
% 1.34/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Y, Z ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.34/1.73 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 T, Y ), Z = Y }.
% 1.34/1.73 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 T, Y ), Z = Y }.
% 1.34/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Y, T ), Z = Y }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ) ) = X }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), X ) = X }.
% 1.34/1.73 { ! X = c_Nat_OSuc( X ) }.
% 1.34/1.73 { ! c_Nat_OSuc( X ) = X }.
% 1.34/1.73 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.34/1.73 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.34/1.73 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.34/1.73 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.34/1.73 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.34/1.73 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.34/1.73 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 1.34/1.73 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.34/1.73 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.34/1.73 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { c_Nat_Onat_Onat__size( c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, c_Nat_Onat_Onat__size( X ), c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 1.34/1.73 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 1.34/1.73 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 1.34/1.73 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.34/1.73 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 1.34/1.73 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.34/1.73 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.34/1.73 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 1.34/1.73 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 1.34/1.73 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.34/1.73 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 1.34/1.73 tc_Nat_Onat, X ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.34/1.73 ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.34/1.73 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 1.34/1.73 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.34/1.73 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.34/1.73 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.34/1.73 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.34/1.73 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.34/1.73 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.34/1.73 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.34/1.73 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.34/1.73 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.34/1.73 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 1.34/1.73 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.34/1.73 ), U = Z, T = Y }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.34/1.73 ) ), Z ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.34/1.73 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.34/1.73 ), ! U = T }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.34/1.73 ), ! Z = Y }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.34/1.73 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.34/1.73 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.34/1.73 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.34/1.73 ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.34/1.73 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.34/1.73 }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.34/1.73 c_Nat_OSuc( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.34/1.73 ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.34/1.73 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.34/1.73 , c_Nat_OSuc( X ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol2( X, Y ) ) }.
% 1.34/1.73 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.34/1.73 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.34/1.73 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.34/1.73 ) ) }.
% 1.34/1.73 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Z, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Y, Z ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.34/1.73 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.34/1.73 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.34/1.73 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 1.34/1.73 Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 1.34/1.73 , c_Polynomial_Odegree( X, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.34/1.73 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 1.34/1.73 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.34/1.73 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 1.34/1.73 c_Polynomial_Odegree( X, Z ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.34/1.73 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.34/1.73 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( X ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__semiring( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__semiring( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__semiring( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__semiring( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.34/1.73 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.34/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.34/1.73 .
% 1.34/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.34/1.73 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.34/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.34/1.73 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.73 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.34/1.73 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.73 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.73 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 1.34/1.73 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.73 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.34/1.73 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.34/1.73 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.34/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.34/1.73 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.34/1.73 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.34/1.73 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.34/1.73 ), X ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.73 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.34/1.73 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.34/1.73 ) ), T ), Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.34/1.73 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha3( X, Y
% 1.34/1.73 , Z ), alpha26( X, Y, Z ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha26( X, Y, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), alpha26( X, Y, Z ) }.
% 1.34/1.73 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.34/1.73 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), alpha3( X, Y, Z ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( X ) ), alpha4( X, Y, Z ), alpha27( X, Y, Z ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( X ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha27( X, Y, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( X ) ) }.
% 1.34/1.73 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( X ), Y ), alpha27( X, Y, Z ) }.
% 1.34/1.73 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.34/1.73 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), alpha4( X, Y, Z ) }.
% 1.34/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( X ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.34/1.73 , Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol3( X, Y ) ) }.
% 1.34/1.73 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.34/1.73 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.34/1.73 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.34/1.73 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.34/1.73 hAPP( Y, U ) ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.34/1.73 ( Z, skol4( X, Y, Z ) ), hAPP( Y, skol4( X, Y, Z ) ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.34/1.73 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.34/1.73 hAPP( Y, U ) ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.34/1.73 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.34/1.73 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.34/1.73 hAPP( Y, U ) ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.34/1.73 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.34/1.73 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.34/1.73 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.34/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.34/1.73 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.34/1.73 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 1.34/1.73 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 1.34/1.73 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 1.34/1.73 , Y ) ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.73 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { c_HOL_Obool_Obool__size( c_fTrue ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ) }.
% 1.34/1.73 { c_HOL_Obool_Obool__size( c_fFalse ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.34/1.73 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.34/1.73 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.34/1.73 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.34/1.73 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.34/1.73 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.73 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.34/1.73 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.73 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.34/1.73 , Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.34/1.73 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.34/1.73 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.34/1.73 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 1.34/1.73 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.34/1.73 , Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.34/1.73 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.34/1.73 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.73 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.34/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.34/1.73 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.34/1.73 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.34/1.73 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.34/1.73 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.34/1.73 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.34/1.73 ), Y ) }.
% 1.34/1.73 { c_Nat_Osize__class_Osize( tc_HOL_Obool, c_fFalse ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { c_Nat_Osize__class_Osize( tc_HOL_Obool, c_fTrue ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 hAPP( Y, skol5( X, Y ) ), hAPP( Y, c_Nat_OSuc( skol5( X, Y ) ) ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.34/1.73 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.73 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.34/1.73 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.34/1.73 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.34/1.73 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.34/1.73 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.34/1.73 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.34/1.73 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.34/1.73 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.34/1.73 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.34/1.73 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.34/1.73 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 1.34/1.73 ( X ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.34/1.73 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.34/1.73 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.34/1.73 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Nat_Onat ) ) = Y }.
% 1.34/1.73 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.34/1.73 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.34/1.73 c_Polynomial_Ocoeff( X, Y ) }.
% 1.34/1.73 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.34/1.73 ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.34/1.73 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol6( X
% 1.34/1.73 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol6( X, Y, Z ) ), Z = Y
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.34/1.73 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.34/1.73 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.34/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.34/1.73 = Y }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( X ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Y ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 = Y }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.34/1.73 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.34/1.73 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.34/1.73 ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.34/1.73 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.34/1.73 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.34/1.73 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.34/1.73 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Z, Y ) ) = Y }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.34/1.73 Y ) ) = Y }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.34/1.73 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.34/1.73 = Y }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.34/1.73 = Y }.
% 1.34/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.34/1.73 = Y }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.34/1.73 = Y }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.34/1.73 = Y }.
% 1.34/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.34/1.73 = Y }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.34/1.73 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.73 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.34/1.73 c_Polynomial_Odegree( X, Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.34/1.73 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Nat_Onat ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Nat_Onat ) }.
% 1.34/1.73 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.34/1.73 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.73 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.34/1.73 , Y ), X ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 1.34/1.73 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Y ), Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.34/1.73 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.34/1.73 Z ) = Y }.
% 1.34/1.73 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.34/1.73 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Y ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Z, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.34/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.34/1.73 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.34/1.73 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ) ) = Z }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.34/1.73 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.34/1.73 ), Y ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.34/1.73 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 1.34/1.73 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.34/1.73 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.34/1.73 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.34/1.73 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 1.34/1.73 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.34/1.73 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.34/1.73 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.34/1.73 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.34/1.73 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.34/1.73 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.73 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.34/1.73 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.34/1.73 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.34/1.73 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.34/1.73 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.34/1.73 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.34/1.73 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.34/1.73 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.34/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.34/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.34/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.34/1.73 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.34/1.73 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.34/1.73 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.73 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Y ), Z = Y }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Nat_Onat ) ) = Y }.
% 1.34/1.73 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( X ) }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.34/1.73 = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.34/1.73 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.34/1.73 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.34/1.73 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Z ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.34/1.73 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.34/1.73 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.34/1.73 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.34/1.73 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.34/1.73 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.34/1.73 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.34/1.73 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.34/1.73 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.34/1.73 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.34/1.73 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.34/1.73 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.34/1.73 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.34/1.73 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.34/1.73 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 1.34/1.73 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.34/1.73 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.34/1.73 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.34/1.73 Y ) ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.34/1.73 Y ) ) ), Y ) }.
% 1.34/1.73 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.34/1.73 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.34/1.73 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.34/1.73 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.34/1.73 ( tc_Int_Oint ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.73 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.73 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.73 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.73 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.73 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.73 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.73 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.73 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.73 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.34/1.73 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.34/1.73 , Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.34/1.73 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 1.34/1.73 , Z, Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.34/1.73 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 1.34/1.73 ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.73 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.34/1.73 Z, T ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.34/1.73 ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), X ) = X }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ) ) = X }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.34/1.73 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.34/1.73 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.34/1.73 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.34/1.73 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.34/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.34/1.73 ), T ), U ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.73 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.34/1.73 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.34/1.73 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 1.34/1.73 X, T, Z ), Y ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.34/1.73 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.34/1.73 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.34/1.73 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.34/1.73 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha5( X
% 1.34/1.73 , Y, T ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha28( X
% 1.34/1.73 , Y, Z, T ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), ! alpha5( X, Y, T ), ! alpha28( X, Y, Z, T )
% 1.34/1.73 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 1.34/1.73 ( X, T, Z ), Y ) }.
% 1.34/1.73 { ! alpha28( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.34/1.73 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha28( X, Y, Z, T ) }.
% 1.34/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha28( X
% 1.34/1.73 , Y, Z, T ) }.
% 1.34/1.73 { ! alpha5( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.73 { Z = c_Groups_Ozero__class_Ozero( X ), alpha5( X, Y, Z ) }.
% 1.34/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha5( X
% 1.34/1.73 , Y, Z ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.34/1.73 ( X ), Z, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X )
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree
% 1.34/1.73 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.34/1.73 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.34/1.73 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.34/1.73 ) ) }.
% 1.34/1.73 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.34/1.73 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.34/1.73 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.34/1.73 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.34/1.73 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.34/1.73 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 1.34/1.73 ) ) }.
% 1.34/1.73 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Y ), Z = Y }.
% 1.34/1.73 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Y ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.34/1.73 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.34/1.73 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 1.34/1.73 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.34/1.73 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 1.34/1.73 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.34/1.73 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 1.34/1.73 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.34/1.73 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.34/1.73 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.34/1.73 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.34/1.73 hAPP( Z, skol7( U, W, Z ) ) ) }.
% 1.34/1.73 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.34/1.73 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol7( X
% 1.34/1.73 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.73 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 1.34/1.73 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 1.34/1.73 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol14( X,
% 1.34/1.73 Y, Z ) ) ) ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.34/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.34/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.34/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.34/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.34/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.34/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.34/1.73 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 1.34/1.73 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 1.34/1.73 , Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.34/1.73 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.34/1.73 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.34/1.73 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.73 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.34/1.73 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.34/1.73 X ) ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.34/1.73 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.34/1.73 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.34/1.73 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.34/1.73 ( tc_Int_Oint ) ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.34/1.73 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.34/1.73 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.34/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.73 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.34/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.34/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.73 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 1.34/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Int_Oint, Y, X ) }.
% 1.34/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.34/1.73 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 1.34/1.73 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 1.34/1.73 ) ) }.
% 1.34/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.34/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.34/1.73 X, W, Z ) ), U ), T ), Y ) }.
% 1.34/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), Z ), U ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.34/1.73 ( X, Z, W ) ), U ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.73 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.34/1.73 , ! alpha6( X, Y, Z ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.34/1.73 , ! alpha29( X, Y, Z ) }.
% 1.34/1.73 { alpha6( X, Y, Z ), alpha29( X, Y, Z ), hBOOL( hAPP( Z,
% 1.34/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.34/1.73 { ! alpha29( X, Y, Z ), ! hBOOL( hAPP( Z, skol8( T, U, Z ) ) ) }.
% 1.34/1.73 { ! alpha29( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.34/1.73 skol8( X, Y, Z ) ) }.
% 1.34/1.73 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.34/1.73 ) ), alpha29( X, Y, Z ) }.
% 1.34/1.73 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! alpha6( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ) ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6( X, Y, Z ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.34/1.73 , alpha7( X, Y, Z ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.34/1.73 , alpha30( X, Y, Z ) }.
% 1.34/1.73 { ! alpha7( X, Y, Z ), ! alpha30( X, Y, Z ), hBOOL( hAPP( Z,
% 1.34/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.34/1.73 { ! alpha30( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.34/1.73 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Z, skol9( T, U, Z ) ) ), alpha30( X, Y, Z ) }.
% 1.34/1.73 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol9( X, Y, Z ) ),
% 1.34/1.73 alpha30( X, Y, Z ) }.
% 1.34/1.73 { ! alpha7( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.34/1.73 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha7( X, Y, Z ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha7
% 1.34/1.73 ( X, Y, Z ) }.
% 1.34/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.34/1.73 ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.34/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.34/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.34/1.73 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.34/1.73 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.34/1.73 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.34/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.34/1.73 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 1.34/1.73 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 1.34/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.34/1.73 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 1.34/1.73 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.34/1.73 .
% 1.34/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.34/1.73 ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.34/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 1.34/1.73 ( tc_Int_Oint, Y, X ), X = Y }.
% 1.34/1.73 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.34/1.73 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.73 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.34/1.73 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 1.34/1.73 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 1.34/1.73 hAPP( Z, Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.34/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Z, X ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.34/1.73 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.34/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.34/1.73 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, Z, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, Z, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.34/1.73 , T ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , T, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , Y, T ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, Z, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , T, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, T, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , Y, Z ) ) }.
% 1.34/1.73 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.34/1.73 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.34/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.34/1.73 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.34/1.73 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.34/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.34/1.73 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.34/1.73 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.34/1.73 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.34/1.73 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.34/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.34/1.73 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.34/1.73 ( X, Y ), Z ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.39/1.73 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.39/1.73 ( X, Z ), Y ) }.
% 1.39/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.39/1.73 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.39/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.39/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.39/1.73 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.39/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 1.39/1.73 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.73 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.39/1.73 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.73 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.39/1.73 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.73 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.39/1.73 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.39/1.73 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.39/1.73 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.73 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.39/1.73 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.73 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.39/1.73 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.39/1.73 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.39/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.39/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.39/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.39/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.39/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.39/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.39/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.73 tc_Nat_Onat ), X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.73 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.39/1.73 .
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.39/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.39/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.39/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.73 tc_Nat_Onat ), X ) }.
% 1.39/1.73 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.39/1.73 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.39/1.73 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.39/1.73 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.39/1.73 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.39/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.39/1.73 .
% 1.39/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.39/1.73 .
% 1.39/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.39/1.73 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.39/1.73 X ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.39/1.73 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.39/1.73 }.
% 1.39/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.39/1.73 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.39/1.73 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 1.39/1.73 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.39/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.39/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.39/1.73 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.39/1.73 , X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.39/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.73 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.39/1.73 .
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.73 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.39/1.73 .
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.39/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.39/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.39/1.73 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.39/1.73 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.73 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.39/1.73 .
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.39/1.73 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.39/1.73 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.39/1.73 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.39/1.73 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 1.39/1.73 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.39/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.39/1.73 Y ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.39/1.73 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.73 Y ), ! Z = Y }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.39/1.73 Z ), ! Z = Y }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.39/1.73 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.39/1.73 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.39/1.73 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.39/1.73 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.39/1.73 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.39/1.73 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.39/1.73 , ! Z = Y }.
% 1.39/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.39/1.73 , ! Z = Y }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.39/1.73 , ! Y = Z }.
% 1.39/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.39/1.73 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.39/1.73 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.39/1.73 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.39/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.39/1.73 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.39/1.73 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.39/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.39/1.73 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.39/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.39/1.73 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.39/1.73 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.39/1.73 ( X ) ) }.
% 1.39/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.39/1.73 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.39/1.73 , Z, Y ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.39/1.73 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.73 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.73 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.39/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.39/1.73 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.39/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.39/1.73 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 1.39/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 1.39/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 1.39/1.73 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 1.39/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.39/1.73 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 1.39/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.39/1.73 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.39/1.73 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.39/1.73 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.39/1.73 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.39/1.73 ) }.
% 1.39/1.73 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.39/1.73 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.39/1.73 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.39/1.73 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.39/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.73 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.39/1.73 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.73 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.39/1.73 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.39/1.73 { alpha58( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.39/1.73 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.39/1.73 { alpha58( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.39/1.73 ( X, Y ), Z ) ) }.
% 1.39/1.73 { ! alpha58( X, Y, Z ), alpha60( X, Y, Z ), Z = Y }.
% 1.39/1.73 { ! alpha58( X, Y, Z ), alpha60( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.39/1.73 ) ) }.
% 1.39/1.73 { ! alpha60( X, Y, Z ), alpha58( X, Y, Z ) }.
% 1.39/1.73 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha58( X, Y, Z ) }.
% 1.39/1.73 { ! alpha60( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.39/1.73 }.
% 1.39/1.73 { ! alpha60( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.39/1.73 X, Y ), Z ) ), alpha60( X, Y, Z ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.39/1.73 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.39/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.39/1.73 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.39/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.39/1.73 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.39/1.73 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.39/1.73 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.73 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.39/1.73 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.39/1.73 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 1.39/1.73 }.
% 1.39/1.73 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.39/1.73 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.39/1.73 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.39/1.73 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.39/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.39/1.73 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.39/1.73 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.39/1.73 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.39/1.73 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.39/1.73 X, Y, Z ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.39/1.73 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.39/1.73 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.39/1.73 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.39/1.73 ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.39/1.73 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.39/1.73 ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.39/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.39/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.39/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.39/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.39/1.73 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.39/1.73 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.39/1.73 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.39/1.73 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.39/1.73 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.39/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.39/1.73 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.39/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.73 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.39/1.73 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.39/1.73 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.39/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.73 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.73 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.73 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.39/1.73 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.39/1.73 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.39/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.39/1.73 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.39/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.39/1.73 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.39/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.39/1.73 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.39/1.73 ( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.73 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.73 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.73 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.39/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.39/1.73 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.39/1.73 , ! Z = Y }.
% 1.39/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.39/1.73 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.39/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.39/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.39/1.73 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.39/1.73 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.39/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.73 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.39/1.73 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.39/1.73 .
% 1.39/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.39/1.73 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.39/1.73 }.
% 1.39/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.39/1.73 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.39/1.73 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.39/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.39/1.73 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.39/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.39/1.73 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.39/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.39/1.73 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.39/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.39/1.73 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.39/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.73 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.39/1.73 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.39/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.39/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.74 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.39/1.74 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.39/1.74 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.39/1.74 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.39/1.74 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.39/1.74 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.39/1.74 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.39/1.74 ) }.
% 1.39/1.74 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.39/1.74 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.39/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.39/1.74 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.39/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.39/1.74 ) ) = X }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.39/1.74 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.39/1.74 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.39/1.74 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.39/1.74 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.39/1.74 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.39/1.74 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.39/1.74 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.39/1.74 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.39/1.74 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.39/1.74 ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.39/1.74 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 1.39/1.74 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 1.39/1.74 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.39/1.74 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.39/1.74 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.39/1.74 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.39/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.39/1.74 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.39/1.74 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.39/1.74 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.39/1.74 Z ) ), Y ) ) }.
% 1.39/1.74 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.39/1.74 Z ) ), U ), T ) = Y }.
% 1.39/1.74 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.39/1.74 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( X ), Z ), U ), Y ) }.
% 1.39/1.74 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.39/1.74 W ) ), U ), Y ) }.
% 1.39/1.74 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.39/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.39/1.74 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( X ), Z ), U ), Y ) }.
% 1.39/1.74 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.39/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.39/1.74 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.39/1.74 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.39/1.74 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.39/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.39/1.74 }.
% 1.39/1.74 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.39/1.74 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.39/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.39/1.74 }.
% 1.39/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.39/1.74 X, Y ) }.
% 1.39/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.39/1.74 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.39/1.74 X, Z, Y ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.39/1.74 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.39/1.74 X, Y ) ) }.
% 1.39/1.74 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.39/1.74 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.39/1.74 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.39/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.39/1.74 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.39/1.74 , Y ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.39/1.74 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha8( X, Y, Z, T ),
% 1.39/1.74 alpha31( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z, T ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha31( X, Y, Z, T ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha31( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.39/1.74 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.39/1.74 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha8( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha9( X, Y, Z, T ),
% 1.39/1.74 alpha32( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha32( X, Y, Z, T ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.39/1.74 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha32( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.39/1.74 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.39/1.74 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha9( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.39/1.74 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.39/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.39/1.74 .
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.39/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.39/1.74 .
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.39/1.74 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.39/1.74 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.39/1.74 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.39/1.74 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.39/1.74 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.39/1.74 ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.39/1.74 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.39/1.74 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.39/1.74 ) ) }.
% 1.39/1.74 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.39/1.74 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.39/1.74 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.39/1.74 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.39/1.74 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.39/1.74 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.39/1.74 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.39/1.74 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.39/1.74 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.39/1.74 , Y, T ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.39/1.74 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.39/1.74 .
% 1.39/1.74 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.39/1.74 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , Y ) }.
% 1.39/1.74 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.39/1.74 , Y ) }.
% 1.39/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.39/1.74 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.39/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.39/1.74 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.39/1.74 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.39/1.74 .
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.39/1.74 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.39/1.74 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.39/1.74 , Z ), X ) ), T ) ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Int_Oint, U, T ) ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.39/1.74 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.39/1.74 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.39/1.74 ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.39/1.74 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.39/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.39/1.74 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.39/1.74 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.39/1.74 X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, Z, Y ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, Z, X ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.39/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.39/1.74 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.39/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.39/1.74 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.39/1.74 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.39/1.74 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.74 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 1.39/1.74 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.39/1.74 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.39/1.74 c_Nat_OSuc( X ) ) }.
% 1.39/1.74 { ! alpha10( X, Y ), Y = c_Nat_OSuc( skol10( Z, Y ) ) }.
% 1.39/1.74 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol10( X
% 1.39/1.74 , Y ), X ) }.
% 1.39/1.74 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.39/1.74 ), alpha10( X, Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.39/1.74 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol11( X ) ) }.
% 1.39/1.74 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.39/1.74 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.39/1.74 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 1.39/1.74 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.39/1.74 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, Y, X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, Y, X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol12( X, Y ) ) ) }.
% 1.39/1.74 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.39/1.74 .
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.39/1.74 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.39/1.74 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.39/1.74 tc_Nat_Onat ), X ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.39/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.39/1.74 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.39/1.74 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.39/1.74 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), Z ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.39/1.74 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.39/1.74 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 Y ), X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.39/1.74 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.39/1.74 ), X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.39/1.74 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.39/1.74 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.39/1.74 = X }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.39/1.74 tc_Int_Oint ) ) ) }.
% 1.39/1.74 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.39/1.74 tc_Int_Oint ) ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.39/1.74 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.39/1.74 }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.39/1.74 tc_Int_Oint ) ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.39/1.74 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.39/1.74 }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.39/1.74 tc_Int_Oint ) ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.39/1.74 tc_Int_Oint ) ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.39/1.74 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.39/1.74 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.39/1.74 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.39/1.74 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.39/1.74 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.39/1.74 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.39/1.74 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.39/1.74 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.39/1.74 ), X ) ) }.
% 1.39/1.74 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.39/1.74 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.39/1.74 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 1.39/1.74 .
% 1.39/1.74 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.39/1.74 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.39/1.74 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.39/1.74 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.39/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.74 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.39/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.74 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.39/1.74 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.39/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.74 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.39/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.74 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.39/1.74 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.39/1.74 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.39/1.74 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.39/1.74 .
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.39/1.74 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.39/1.74 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.39/1.74 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.39/1.74 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.39/1.74 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.39/1.74 ) ) }.
% 1.39/1.74 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.39/1.74 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.39/1.74 ) ) }.
% 1.39/1.74 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.39/1.74 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.39/1.74 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.39/1.74 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.39/1.74 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.39/1.74 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.39/1.74 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.39/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.39/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.39/1.74 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.39/1.74 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.39/1.74 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.39/1.74 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.39/1.74 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.39/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.39/1.74 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.39/1.74 ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.39/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.39/1.74 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.39/1.74 ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.39/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.39/1.74 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.39/1.74 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 1.39/1.74 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.39/1.74 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 1.39/1.74 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 1.39/1.74 tc_Nat_Onat ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.39/1.74 c_Groups_Oone__class_Oone( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.39/1.74 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.39/1.74 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.39/1.74 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.39/1.74 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.39/1.74 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.39/1.74 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.39/1.74 ( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.39/1.74 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.39/1.74 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.39/1.74 ( tc_Nat_Onat ) ) ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.39/1.74 ( tc_Int_Oint ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.39/1.74 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.39/1.74 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.39/1.74 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.39/1.74 c_Groups_Oone__class_Oone( X ) }.
% 1.39/1.74 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.39/1.74 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.39/1.74 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.39/1.74 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Nat_Onat, Y, Z ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, Z, Y ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 1.39/1.74 , Z ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 1.39/1.74 Z, Y ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 1.39/1.74 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 1.39/1.74 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.39/1.74 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Nat_Onat, Y, Z ) }.
% 1.39/1.74 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, Z, Y ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Nat_Onat, Y, Z ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.39/1.74 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, Y, X ), Y = X }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.39/1.74 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.39/1.74 { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! alpha11( X, Y ), ! Y = X }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha11( X, Y ) }
% 1.39/1.74 .
% 1.39/1.74 { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! alpha11( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), alpha11( X, Y ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha12( X, Y ), Y = X }
% 1.39/1.74 .
% 1.39/1.74 { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! alpha12( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.39/1.74 ( tc_Nat_Onat, X, Y ), alpha12( X, Y ) }.
% 1.39/1.74 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.39/1.74 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.39/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.39/1.74 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.39/1.74 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.39/1.74 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 1.39/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.39/1.74 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.39/1.74 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.39/1.74 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.39/1.74 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.39/1.74 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.39/1.74 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.39/1.74 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.39/1.74 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.39/1.74 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.39/1.74 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 1.39/1.74 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 1.39/1.74 ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Int_Oint, Z, X ) }.
% 1.39/1.74 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ) ) }.
% 1.39/1.74 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.39/1.74 tc_Nat_Onat ), X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), Y ) }.
% 1.39/1.74 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.39/1.74 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 1.39/1.74 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 1.39/1.74 ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Nat_Onat, Z, X ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.39/1.74 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), Y ) }.
% 1.39/1.74 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.39/1.74 ), X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Int_Oint ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.39/1.74 tc_Int_Oint ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Int_Oint, X, Y ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z, Y ), alpha61( X, Y, Z, T ), ! Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.39/1.74 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z, Y ), alpha61( X, Y, Z, T ), ! hAPP(
% 1.39/1.74 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.39/1.74 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 1.39/1.74 .
% 1.39/1.74 { ! alpha61( X, Y, Z, T ), alpha62( X, Y, Z, T ), alpha59( X, Y, T ) }.
% 1.39/1.74 { ! alpha61( X, Y, Z, T ), alpha62( X, Y, Z, T ), ! hAPP(
% 1.39/1.74 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) }.
% 1.39/1.74 { ! alpha62( X, Y, Z, T ), alpha61( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha59( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.39/1.74 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 alpha61( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha62( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.39/1.74 ( X ), Z, T ), alpha63( X, Y, Z, T ) }.
% 1.39/1.74 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha62( X, Y
% 1.39/1.74 , Z, T ) }.
% 1.39/1.74 { ! alpha63( X, Y, Z, T ), alpha62( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha63( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.39/1.74 ), skol13( X, Y, U, W ), Y ) }.
% 1.39/1.74 { ! alpha63( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.39/1.74 ), skol13( X, Y, U, T ), T ) }.
% 1.39/1.74 { ! alpha63( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.39/1.74 ( X ), skol13( X, Y, Z, T ), Z ) }.
% 1.39/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 1.39/1.74 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha63( X, Y
% 1.39/1.74 , Z, T ) }.
% 1.39/1.74 { ! alpha59( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! alpha59( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha59( X, Y, Z
% 1.39/1.74 ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.39/1.74 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 1.39/1.74 }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.39/1.74 , alpha44( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha44( X, Y, Z, T ),
% 1.39/1.74 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.39/1.74 { ! alpha44( X, Y, Z, T ), alpha13( X, Z, T ) }.
% 1.39/1.74 { ! alpha44( X, Y, Z, T ), alpha33( X, Y, T ) }.
% 1.39/1.74 { ! alpha13( X, Z, T ), ! alpha33( X, Y, T ), alpha44( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha33( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ), alpha45( X, Y, Z ) }.
% 1.39/1.74 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha33( X
% 1.39/1.74 , Y, Z ) }.
% 1.39/1.74 { ! alpha45( X, Y, Z ), alpha33( X, Y, Z ) }.
% 1.39/1.74 { ! alpha45( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.39/1.74 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.39/1.74 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha45( X
% 1.39/1.74 , Y, Z ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.39/1.74 ), c_Polynomial_Odegree( X, Z ) ), alpha45( X, Y, Z ) }.
% 1.39/1.74 { ! alpha13( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha13( X,
% 1.39/1.74 Y, Z ) }.
% 1.39/1.74 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha13( X
% 1.39/1.74 , Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.39/1.74 .
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.39/1.74 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 1.39/1.74 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.39/1.74 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.39/1.74 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.39/1.74 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.39/1.74 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.39/1.74 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.39/1.74 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.39/1.74 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 1.39/1.74 ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.39/1.74 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 1.39/1.74 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 1.39/1.74 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 1.39/1.74 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 1.39/1.74 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 1.39/1.74 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.39/1.74 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Int_Oint, X, Y ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.39/1.74 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.39/1.74 ) }.
% 1.39/1.74 { ! class_RealVector_Oreal__normed__field( X ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.39/1.74 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.39/1.74 ), Y ) }.
% 1.39/1.74 { ! class_RealVector_Oreal__normed__field( X ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.39/1.74 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 1.39/1.74 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.39/1.74 { ! class_RealVector_Oreal__normed__field( X ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 1.39/1.74 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.39/1.74 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 1.39/1.74 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 1.39/1.74 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.39/1.74 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 1.39/1.74 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.39/1.74 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.39/1.74 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.39/1.74 c_Groups_Oone__class_Oone( X ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 1.39/1.74 ( X ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.39/1.74 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.39/1.74 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.39/1.74 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.39/1.74 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.39/1.74 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.39/1.74 { ! class_RealVector_Oreal__normed__field( X ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.39/1.74 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 1.39/1.74 ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.39/1.74 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.39/1.74 tc_Int_Oint, X, Y ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.39/1.74 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 1.39/1.74 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.39/1.74 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.39/1.74 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.39/1.74 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.39/1.74 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.39/1.74 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ), alpha34
% 1.39/1.74 ( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha14( X, Y, Z
% 1.39/1.74 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha34( X, Y, Z
% 1.39/1.74 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.39/1.74 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( X ), Y ), alpha34( X, Y, Z ) }.
% 1.39/1.74 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.39/1.74 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha15( X, Y, Z ), alpha35
% 1.39/1.74 ( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha15( X, Y, Z
% 1.39/1.74 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.39/1.74 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z
% 1.39/1.74 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.39/1.74 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.39/1.74 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.39/1.74 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ), alpha35( X, Y, Z ) }.
% 1.39/1.74 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.39/1.74 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ), alpha15( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha16( X, Y, Z ), alpha36
% 1.39/1.74 ( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha16( X, Y, Z
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.39/1.74 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 ), alpha36( X, Y, Z ) }.
% 1.39/1.74 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.39/1.74 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.39/1.74 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.39/1.74 ), alpha16( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 1.39/1.74 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha17( X, Y, Z ), alpha37( X,
% 1.39/1.74 Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha17( X, Y, Z
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z
% 1.39/1.74 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.39/1.74 ), alpha37( X, Y, Z ) }.
% 1.39/1.74 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.39/1.74 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.39/1.74 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 ), alpha17( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , Y, Z ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , Y, Z ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 1.39/1.74 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha38( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha18( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha38( X, Y, Z, T ), !
% 1.39/1.74 alpha18( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 1.39/1.74 { ! alpha38( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.39/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.39/1.74 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha38( X, Y, Z, T ) }.
% 1.39/1.74 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha38(
% 1.39/1.74 X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha18( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) }.
% 1.39/1.74 { Z = c_Groups_Ozero__class_Ozero( X ), alpha18( X, Y, Z ) }.
% 1.39/1.74 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha18( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha39( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha19( X, Y, T ) }.
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha39( X, Y, Z, T ), !
% 1.39/1.74 alpha19( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.39/1.74 { ! alpha39( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.39/1.74 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.39/1.74 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha39( X, Y, Z, T ) }.
% 1.39/1.74 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha39(
% 1.39/1.74 X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha19( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) }.
% 1.39/1.74 { Y = c_Groups_Ozero__class_Ozero( X ), alpha19( X, Y, Z ) }.
% 1.39/1.74 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha19( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.39/1.74 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.39/1.74 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.39/1.74 X ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.39/1.74 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.39/1.74 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 1.39/1.74 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.39/1.74 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.39/1.74 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.39/1.74 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.39/1.74 X ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.39/1.74 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.39/1.74 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 Z, Y ) ), alpha40( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 Z, Y ) ), alpha46( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha40( X, Y, Z
% 1.39/1.74 , T ), ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.39/1.74 { ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ), alpha50( X, Y, Z, T ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.39/1.74 , alpha46( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha50( X, Y, Z, T ), alpha46( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha50( X, Y, Z, T ), alpha54( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha50( X, Y, Z, T ), alpha20( X, Y, T ) }.
% 1.39/1.74 { ! alpha54( X, Y, Z, T ), ! alpha20( X, Y, T ), alpha50( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha54( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 alpha54( X, Y, Z, T ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha54( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha40( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 alpha40( X, Y, Z, T ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha40( X, Y, Z, T )
% 1.39/1.74 }.
% 1.39/1.74 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 , alpha20( X, Y, Z ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 , alpha20( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.39/1.74 Z ), Y ), alpha41( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.39/1.74 Z ), Y ), alpha47( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha41( X, Y, Z
% 1.39/1.74 , T ), ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.39/1.74 { ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Z ), alpha51( X, Y, Z, T ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.39/1.74 , alpha47( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha51( X, Y, Z, T ), alpha47( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha51( X, Y, Z, T ), alpha55( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha51( X, Y, Z, T ), alpha21( X, Y, Z ) }.
% 1.39/1.74 { ! alpha55( X, Y, Z, T ), ! alpha21( X, Y, Z ), alpha51( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha55( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 alpha55( X, Y, Z, T ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha55( X, Y, Z, T )
% 1.39/1.74 }.
% 1.39/1.74 { ! alpha41( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.39/1.74 alpha41( X, Y, Z, T ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha41( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 , alpha21( X, Y, Z ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.39/1.74 , alpha21( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.39/1.74 Y ), Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.39/1.74 Y ), Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.39/1.74 Y ), Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.39/1.74 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.39/1.74 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.39/1.74 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.39/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 1.39/1.74 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.39/1.74 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 1.39/1.74 .
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 1.39/1.74 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 1.39/1.74 .
% 1.39/1.74 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.39/1.74 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 1.39/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.39/1.74 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.39/1.74 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.39/1.74 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.39/1.74 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, Z, Y ) ), alpha42( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, Z, Y ) ), alpha48( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha42( X, Y, Z
% 1.39/1.74 , T ), ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.39/1.74 { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ), alpha52( X, Y, Z, T ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.39/1.74 , alpha48( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha52( X, Y, Z, T ), alpha48( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha52( X, Y, Z, T ), alpha56( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha52( X, Y, Z, T ), alpha22( X, Y, T ) }.
% 1.39/1.74 { ! alpha56( X, Y, Z, T ), ! alpha22( X, Y, T ), alpha52( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha56( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.74 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 alpha56( X, Y, Z, T ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha56( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha42( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 1.39/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.39/1.74 alpha42( X, Y, Z, T ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha42( X, Y, Z, T )
% 1.39/1.74 }.
% 1.39/1.74 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.74 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 , alpha22( X, Y, Z ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.39/1.74 ) ), alpha22( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , T, Z ), Y ), alpha43( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , T, Z ), Y ), alpha49( X, Y, Z, T ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha43( X, Y, Z
% 1.39/1.74 , T ), ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.39/1.74 { ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Z ), alpha53( X, Y, Z, T ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.39/1.74 , alpha49( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha53( X, Y, Z, T ), alpha49( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha53( X, Y, Z, T ), alpha57( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha53( X, Y, Z, T ), alpha23( X, Y, Z ) }.
% 1.39/1.74 { ! alpha57( X, Y, Z, T ), ! alpha23( X, Y, Z ), alpha53( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha57( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.74 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.39/1.74 alpha57( X, Y, Z, T ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha57( X, Y, Z, T )
% 1.39/1.74 }.
% 1.39/1.74 { ! alpha43( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 1.39/1.74 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.39/1.74 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.39/1.74 alpha43( X, Y, Z, T ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha43( X, Y, Z, T ) }.
% 1.39/1.74 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.39/1.74 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.39/1.74 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.39/1.74 , alpha23( X, Y, Z ) }.
% 1.39/1.74 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.39/1.74 , Y ), alpha23( X, Y, Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , T, Y ), Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , T, Y ), Z ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.39/1.74 ( X, Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.39/1.74 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.39/1.74 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , T, Y ), Z ) }.
% 1.39/1.74 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 1.39/1.74 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.39/1.74 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 1.39/1.74 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.39/1.74 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.39/1.74 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T, Z ), Y ) =
% 1.39/1.74 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.39/1.74 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Polynomial_Osmult( X,
% 1.39/1.74 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 1.39/1.74 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ),
% 1.39/1.74 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y )
% 1.39/1.74 ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.39/1.74 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.39/1.74 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.39/1.74 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 1.39/1.74 ( X ), Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.39/1.74 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 1.39/1.74 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.39/1.74 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 1.39/1.74 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.39/1.74 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 1.39/1.74 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.39/1.74 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 1.39/1.74 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 1.39/1.74 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.39/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.39/1.74 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 1.39/1.74 ( X, Z, Y ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.39/1.74 ( X ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__add(
% 1.39/1.74 X ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ocomm__monoid__add( X
% 1.39/1.74 ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring( X ) }
% 1.39/1.74 .
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Omonoid__add( X ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0( X ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero( X ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring( X ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ozero( X ) }.
% 1.39/1.74 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.39/1.74 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.39/1.74 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.39/1.74 ( tc_fun( Y, X ) ) }.
% 1.39/1.74 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.39/1.74 ) ) }.
% 1.39/1.74 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.39/1.74 .
% 1.39/1.74 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.39/1.74 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.39/1.74 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.39/1.74 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.39/1.74 tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.39/1.74 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.39/1.74 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.39/1.74 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.39/1.74 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.39/1.74 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.39/1.74 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.39/1.74 { class_Power_Opower( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.39/1.74 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.39/1.74 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.39/1.74 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.39/1.74 tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.39/1.74 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.39/1.74 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.39/1.74 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.39/1.74 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.39/1.74 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.39/1.74 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.39/1.74 { ! class_Rings_Oidom( X ),
% 1.39/1.74 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.39/1.74 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.39/1.74 ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.39/1.74 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.39/1.74 X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.39/1.74 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.39/1.74 ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.39/1.74 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.39/1.74 }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.39/1.74 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.39/1.74 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.39/1.74 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.39/1.74 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.39/1.74 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.39/1.74 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.39/1.74 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.39/1.74 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.39/1.74 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.39/1.74 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.39/1.74 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.39/1.74 ( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.39/1.74 ( tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.39/1.74 }.
% 1.39/1.74 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.39/1.74 ) ) }.
% 1.39/1.74 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.39/1.74 .
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.39/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.39/1.74 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.39/1.74 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.39/1.74 { ! hBOOL( c_fFalse ) }.
% 1.39/1.74 { hBOOL( c_fTrue ) }.
% 1.39/1.74 { c_Polynomial_Odegree( t_a,
% 1.39/1.74 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a, v_p, v_h )
% 1.39/1.74 ) = c_Polynomial_Odegree( t_a, v_p ) }.
% 1.39/1.74 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) }.
% 1.39/1.74 { ! c_Polynomial_Odegree( t_a, c_Groups_Oplus__class_Oplus(
% 1.39/1.74 tc_Polynomial_Opoly( t_a ), c_Polynomial_Osmult( t_a, v_h,
% 1.39/1.74 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a, v_p, v_h )
% 1.39/1.74 ), c_Polynomial_OpCons( t_a, v_a,
% 1.39/1.74 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a, v_p, v_h )
% 1.39/1.74 ) ) ) = c_Nat_OSuc( c_Polynomial_Odegree( t_a, v_p ) ) }.
% 1.39/1.74 { class_Rings_Ocomm__semiring__0( t_a ) }.
% 1.39/1.74
% 1.39/1.74 *** allocated 15000 integers for clauses
% 1.39/1.74 *** allocated 22500 integers for clauses
% 1.39/1.74 *** allocated 33750 integers for clauses
% 1.39/1.74 *** allocated 50625 integers for clauses
% 1.39/1.74 *** allocated 75937 integers for clauses
% 1.39/1.74 percentage equality = 0.255951, percentage horn = 0.890482
% 1.39/1.74 This is a problem with some equality
% 1.39/1.74
% 1.39/1.74
% 1.39/1.74
% 1.39/1.74 Options Used:
% 1.39/1.74
% 1.39/1.74 useres = 1
% 1.39/1.74 useparamod = 1
% 1.39/1.74 useeqrefl = 1
% 1.39/1.74 useeqfact = 1
% 1.39/1.74 usefactor = 1
% 1.39/1.74 usesimpsplitting = 0
% 1.39/1.74 usesimpdemod = 5
% 1.39/1.74 usesimpres = 3
% 1.39/1.74
% 1.39/1.74 resimpinuse = 1000
% 1.39/1.74 resimpclauses = 20000
% 1.39/1.74 substype = eqrewr
% 1.39/1.74 backwardsubs = 1
% 1.39/1.74 selectoldest = 5
% 1.39/1.74
% 1.39/1.74 litorderings [0] = split
% 1.39/1.74 litorderings [1] = extend the termordering, first sorting on arguments
% 1.39/1.74
% 1.39/1.74 termordering = kbo
% 1.39/1.74
% 1.39/1.74 litapriori = 0
% 1.39/1.74 termapriori = 1
% 1.39/1.74 litaposteriori = 0
% 1.39/1.74 termaposteriori = 0
% 1.39/1.74 demodaposteriori = 0
% 1.39/1.74 ordereqreflfact = 0
% 1.39/1.74
% 1.39/1.74 litselect = negord
% 1.39/1.74
% 1.39/1.74 maxweight = 15
% 1.39/1.74 maxdepth = 30000
% 1.39/1.74 maxlength = 115
% 1.39/1.74 maxnrvars = 195
% 1.39/1.74 excuselevel = 1
% 1.39/1.74 increasemaxweight = 1
% 1.39/1.74
% 1.39/1.74 maxselected = 10000000
% 1.39/1.74 maxnrclauses = 10000000
% 1.39/1.74
% 1.39/1.74 showgenerated = 0
% 1.39/1.74 showkept = 0
% 1.39/1.74 showselected = 0
% 1.39/1.74 showdeleted = 0
% 1.39/1.74 showresimp = 1
% 1.39/1.74 showstatus = 2000
% 1.39/1.74
% 1.39/1.74 prologoutput = 0
% 1.39/1.74 nrgoals = 5000000
% 1.39/1.74 totalproof = 1
% 1.39/1.74
% 1.39/1.74 Symbols occurring in the translation:
% 1.39/1.74
% 1.39/1.74 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.39/1.74 . [1, 2] (w:1, o:189, a:1, s:1, b:0),
% 1.39/1.74 ! [4, 1] (w:0, o:105, a:1, s:1, b:0),
% 1.39/1.74 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.39/1.74 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.39/1.74 hAPP [38, 2] (w:1, o:213, a:1, s:1, b:0),
% 1.39/1.74 class_Rings_Ocomm__semiring__0 [41, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.39/1.74 tc_Polynomial_Opoly [42, 1] (w:1, o:114, a:1, s:1, b:0),
% 1.39/1.74 c_Groups_Ozero__class_Ozero [43, 1] (w:1, o:115, a:1, s:1, b:0),
% 1.39/1.74 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [44, 3] (w:1
% 1.39/1.74 , o:235, a:1, s:1, b:0),
% 1.39/1.74 c_Polynomial_OpCons [46, 3] (w:1, o:239, a:1, s:1, b:0),
% 1.39/1.74 c_Polynomial_Osmult [51, 3] (w:1, o:240, a:1, s:1, b:0),
% 1.39/1.74 c_Groups_Oplus__class_Oplus [52, 3] (w:1, o:241, a:1, s:1, b:0),
% 1.39/1.74 class_Groups_Ozero [54, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.39/1.74 c_Polynomial_Odegree [55, 2] (w:1, o:215, a:1, s:1, b:0),
% 1.39/1.74 c_Nat_OSuc [56, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.39/1.74 class_Groups_Ocomm__monoid__add [59, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.39/1.74
% 1.39/1.74 class_Rings_Oidom [60, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.39/1.74 tc_Nat_Onat [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.39/1.74 class_Groups_Olinordered__ab__group__add [70, 1] (w:1, o:124, a:1, s:
% 1.39/1.74 1, b:0),
% 1.39/1.74 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [71
% 1.39/1.74 , 1] (w:1, o:155, a:1, s:1, b:0),
% 1.39/1.74 class_Rings_Ocomm__semiring__1 [72, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.39/1.74 class_Groups_Oab__semigroup__add [81, 1] (w:1, o:156, a:1, s:1, b:0)
% 1.39/1.74 ,
% 1.39/1.74 class_Groups_Ocancel__semigroup__add [83, 1] (w:1, o:157, a:1, s:1
% 1.39/1.74 , b:0),
% 1.39/1.74 class_Groups_Ocancel__ab__semigroup__add [84, 1] (w:1, o:158, a:1, s:
% 1.39/1.74 1, b:0),
% 1.39/1.74 class_Groups_Omonoid__add [87, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.39/1.74 c_Polynomial_Opoly__rec [90, 5] (w:1, o:315, a:1, s:1, b:0),
% 1.39/1.74 c_Polynomial_Osynthetic__div [91, 3] (w:1, o:242, a:1, s:1, b:0),
% 1.39/1.74 c_Nat_Onat_Onat__size [93, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.39/1.74 c_fequal [94, 2] (w:1, o:216, a:1, s:1, b:0),
% 1.39/1.74 c_If [95, 4] (w:1, o:286, a:1, s:1, b:0),
% 1.39/1.74 c_Groups_Otimes__class_Otimes [96, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.39/1.74 c_Polynomial_Omonom [97, 3] (w:1, o:243, a:1, s:1, b:0),
% 1.39/1.74 c_Nat_Osize__class_Osize [98, 2] (w:1, o:217, a:1, s:1, b:0),
% 1.39/1.74 c_Orderings_Oord__class_Oless__eq [99, 3] (w:1, o:236, a:1, s:1, b:0)
% 1.39/1.74 ,
% 1.39/1.74 class_Groups_Oab__semigroup__mult [106, 1] (w:1, o:162, a:1, s:1, b:0
% 1.39/1.74 ),
% 1.39/1.74 class_Rings_Olinordered__ring__strict [108, 1] (w:1, o:126, a:1, s:1
% 1.39/1.74 , b:0),
% 1.39/1.74 class_Rings_Olinordered__ring [109, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.39/1.74 class_Groups_Oordered__ab__semigroup__add__imp__le [112, 1] (w:1, o:
% 1.39/1.75 163, a:1, s:1, b:0),
% 1.39/1.75 class_Groups_Oordered__ab__semigroup__add [113, 1] (w:1, o:164, a:1
% 1.39/1.75 , s:1, b:0),
% 1.39/1.75 class_Groups_Oordered__comm__monoid__add [117, 1] (w:1, o:165, a:1
% 1.39/1.75 , s:1, b:0),
% 1.39/1.75 c_Polynomial_Opcompose [118, 3] (w:1, o:244, a:1, s:1, b:0),
% 1.39/1.75 class_Rings_Oordered__cancel__semiring [119, 1] (w:1, o:129, a:1, s:1
% 1.39/1.75 , b:0),
% 1.39/1.75 class_Rings_Oordered__ring [120, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.39/1.75 class_Rings_Oordered__semiring [121, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.39/1.75
% 1.39/1.75 class_Rings_Oordered__comm__semiring [122, 1] (w:1, o:132, a:1, s:1
% 1.39/1.75 , b:0),
% 1.39/1.75 class_Rings_Omult__zero [123, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.39/1.75 class_Rings_Oring__no__zero__divisors [124, 1] (w:1, o:141, a:1, s:1
% 1.39/1.75 , b:0),
% 1.39/1.75 class_Rings_Ono__zero__divisors [125, 1] (w:1, o:128, a:1, s:1, b:0)
% 1.39/1.75 ,
% 1.39/1.75 class_Rings_Ocomm__semiring [126, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.39/1.75 class_Rings_Osemiring [128, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.39/1.75 class_Orderings_Opreorder [129, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.39/1.75 c_Polynomial_Oorder [132, 3] (w:1, o:238, a:1, s:1, b:0),
% 1.39/1.75 class_RealVector_Oreal__normed__algebra [134, 1] (w:1, o:147, a:1, s:
% 1.39/1.75 1, b:0),
% 1.39/1.75 class_Orderings_Oord [137, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.39/1.75 tc_fun [138, 2] (w:1, o:224, a:1, s:1, b:0),
% 1.39/1.75 class_Orderings_Olinorder [139, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.39/1.75 class_Orderings_Oorder [140, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.39/1.75 c_Polynomial_Opoly [143, 2] (w:1, o:225, a:1, s:1, b:0),
% 1.39/1.75 c_fTrue [144, 0] (w:1, o:83, a:1, s:1, b:0),
% 1.39/1.75 c_HOL_Obool_Obool__size [145, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.39/1.75 c_fFalse [146, 0] (w:1, o:84, a:1, s:1, b:0),
% 1.39/1.75 class_Int_Oring__char__0 [147, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.39/1.75 c_Polynomial_Ocoeff [148, 2] (w:1, o:214, a:1, s:1, b:0),
% 1.39/1.75 class_Rings_Olinordered__semiring__1 [150, 1] (w:1, o:133, a:1, s:1
% 1.39/1.75 , b:0),
% 1.39/1.75 c_Groups_Oone__class_Oone [151, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.39/1.75 tc_HOL_Obool [152, 0] (w:1, o:85, a:1, s:1, b:0),
% 1.39/1.75 class_Rings_Ocomm__ring__1 [154, 1] (w:1, o:110, a:1, s:1, b:0),
% 1.39/1.75 c_Groups_Ouminus__class_Ouminus [155, 2] (w:1, o:226, a:1, s:1, b:0)
% 1.39/1.75 ,
% 1.39/1.75 c_Power_Opower__class_Opower [156, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.39/1.75 class_Rings_Ocomm__ring [157, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.39/1.75 class_Groups_Oab__group__add [158, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.39/1.75 class_Groups_Ogroup__add [159, 1] (w:1, o:175, a:1, s:1, b:0),
% 1.39/1.75 class_Groups_Oone [160, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.39/1.75 class_Rings_Oring__1__no__zero__divisors [161, 1] (w:1, o:143, a:1
% 1.39/1.75 , s:1, b:0),
% 1.39/1.75 class_Groups_Oordered__ab__group__add [162, 1] (w:1, o:177, a:1, s:1
% 1.39/1.75 , b:0),
% 1.39/1.75 class_Rings_Oring [163, 1] (w:1, o:144, a:1, s:1, b:0),
% 1.39/1.75 class_Rings_Ozero__neq__one [164, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.39/1.75 tc_Int_Oint [165, 0] (w:1, o:87, a:1, s:1, b:0),
% 1.39/1.75 class_Groups_Ocomm__monoid__mult [166, 1] (w:1, o:178, a:1, s:1, b:0)
% 1.39/1.75 ,
% 1.39/1.75 class_Groups_Omonoid__mult [167, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.39/1.75 class_Rings_Olinordered__semidom [168, 1] (w:1, o:134, a:1, s:1, b:0)
% 1.39/1.75 ,
% 1.39/1.75 class_Rings_Olinordered__idom [169, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.39/1.75 class_Rings_Oring__1 [171, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.39/1.75 class_Power_Opower [172, 1] (w:1, o:180, a:1, s:1, b:0),
% 1.39/1.75 class_Rings_Osemiring__0 [173, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.39/1.75 c_Power_Opower_Opower [178, 3] (w:1, o:245, a:1, s:1, b:0),
% 1.39/1.75 c_Rings_Odvd__class_Odvd [179, 3] (w:1, o:246, a:1, s:1, b:0),
% 1.39/1.75 class_Lattices_Oboolean__algebra [180, 1] (w:1, o:182, a:1, s:1, b:0)
% 1.39/1.75 ,
% 1.39/1.75 class_Rings_Odvd [181, 1] (w:1, o:150, a:1, s:1, b:0),
% 1.39/1.75 class_Fields_Ofield [182, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.39/1.75 class_Lattices_Oab__semigroup__idem__mult [185, 1] (w:1, o:181, a:1
% 1.39/1.75 , s:1, b:0),
% 1.39/1.75 class_Groups_Ouminus [187, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.39/1.75 hBOOL [189, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.39/1.75 c_Polynomial_Opoly__gcd [190, 3] (w:1, o:247, a:1, s:1, b:0),
% 2.38/2.72 c_Orderings_Oord__class_Oless [191, 3] (w:1, o:237, a:1, s:1, b:0),
% 2.38/2.72 class_Rings_Olinordered__semiring__1__strict [192, 1] (w:1, o:136, a:
% 2.38/2.72 1, s:1, b:0),
% 2.38/2.72 c_Groups_Ominus__class_Ominus [193, 3] (w:1, o:248, a:1, s:1, b:0),
% 2.38/2.72 class_Groups_Ominus [200, 1] (w:1, o:185, a:1, s:1, b:0),
% 2.38/2.72 class_Groups_Oordered__cancel__ab__semigroup__add [203, 1] (w:1, o:
% 2.38/2.72 186, a:1, s:1, b:0),
% 2.38/2.72 class_Rings_Olinordered__semiring__strict [208, 1] (w:1, o:137, a:1
% 2.38/2.72 , s:1, b:0),
% 2.38/2.72 class_Rings_Olinordered__comm__semiring__strict [209, 1] (w:1, o:138
% 2.38/2.72 , a:1, s:1, b:0),
% 2.38/2.72 class_Rings_Olinordered__semiring [212, 1] (w:1, o:139, a:1, s:1, b:0
% 2.38/2.72 ),
% 2.38/2.72 c_Polynomial_Opdivmod__rel [216, 5] (w:1, o:316, a:1, s:1, b:0),
% 2.38/2.72 c_Rings_Oinverse__class_Odivide [221, 3] (w:1, o:249, a:1, s:1, b:0)
% 2.38/2.72 ,
% 2.38/2.72 c_Nat__Transfer_Otsub [222, 2] (w:1, o:227, a:1, s:1, b:0),
% 2.38/2.72 class_RealVector_Oreal__normed__field [223, 1] (w:1, o:151, a:1, s:1
% 2.38/2.72 , b:0),
% 2.38/2.72 class_Rings_Odivision__ring [224, 1] (w:1, o:152, a:1, s:1, b:0),
% 2.38/2.72 class_Rings_Odivision__ring__inverse__zero [225, 1] (w:1, o:153, a:1
% 2.38/2.72 , s:1, b:0),
% 2.38/2.72 class_Fields_Ofield__inverse__zero [226, 1] (w:1, o:117, a:1, s:1, b:
% 2.38/2.72 0),
% 2.38/2.72 class_Fields_Olinordered__field__inverse__zero [227, 1] (w:1, o:118
% 2.38/2.72 , a:1, s:1, b:0),
% 2.38/2.72 class_Fields_Olinordered__field [228, 1] (w:1, o:119, a:1, s:1, b:0)
% 2.38/2.72 ,
% 2.38/2.72 class_RealVector_Oreal__field [229, 1] (w:1, o:154, a:1, s:1, b:0),
% 2.38/2.72 c_Divides_Odiv__class_Omod [230, 3] (w:1, o:250, a:1, s:1, b:0),
% 2.38/2.72 class_Divides_Osemiring__div [231, 1] (w:1, o:187, a:1, s:1, b:0),
% 2.38/2.72 class_Groups_Ocancel__comm__monoid__add [234, 1] (w:1, o:188, a:1, s:
% 2.38/2.72 1, b:0),
% 2.38/2.72 t_a [236, 0] (w:1, o:101, a:1, s:1, b:0),
% 2.38/2.72 v_p [237, 0] (w:1, o:102, a:1, s:1, b:0),
% 2.38/2.72 v_h [238, 0] (w:1, o:103, a:1, s:1, b:0),
% 2.38/2.72 v_a [239, 0] (w:1, o:104, a:1, s:1, b:0),
% 2.38/2.72 alpha1 [240, 2] (w:1, o:228, a:1, s:1, b:1),
% 2.38/2.72 alpha2 [241, 2] (w:1, o:232, a:1, s:1, b:1),
% 2.38/2.72 alpha3 [242, 3] (w:1, o:258, a:1, s:1, b:1),
% 2.38/2.72 alpha4 [243, 3] (w:1, o:265, a:1, s:1, b:1),
% 2.38/2.72 alpha5 [244, 3] (w:1, o:267, a:1, s:1, b:1),
% 2.38/2.72 alpha6 [245, 3] (w:1, o:270, a:1, s:1, b:1),
% 2.38/2.72 alpha7 [246, 3] (w:1, o:272, a:1, s:1, b:1),
% 2.38/2.72 alpha8 [247, 4] (w:1, o:287, a:1, s:1, b:1),
% 2.38/2.72 alpha9 [248, 4] (w:1, o:288, a:1, s:1, b:1),
% 2.38/2.72 alpha10 [249, 2] (w:1, o:229, a:1, s:1, b:1),
% 2.38/2.72 alpha11 [250, 2] (w:1, o:230, a:1, s:1, b:1),
% 2.38/2.72 alpha12 [251, 2] (w:1, o:231, a:1, s:1, b:1),
% 2.38/2.72 alpha13 [252, 3] (w:1, o:273, a:1, s:1, b:1),
% 2.38/2.72 alpha14 [253, 3] (w:1, o:274, a:1, s:1, b:1),
% 2.38/2.72 alpha15 [254, 3] (w:1, o:275, a:1, s:1, b:1),
% 2.38/2.72 alpha16 [255, 3] (w:1, o:276, a:1, s:1, b:1),
% 2.38/2.72 alpha17 [256, 3] (w:1, o:277, a:1, s:1, b:1),
% 2.38/2.72 alpha18 [257, 3] (w:1, o:278, a:1, s:1, b:1),
% 2.38/2.72 alpha19 [258, 3] (w:1, o:279, a:1, s:1, b:1),
% 2.38/2.72 alpha20 [259, 3] (w:1, o:251, a:1, s:1, b:1),
% 2.38/2.72 alpha21 [260, 3] (w:1, o:252, a:1, s:1, b:1),
% 2.38/2.72 alpha22 [261, 3] (w:1, o:253, a:1, s:1, b:1),
% 2.38/2.72 alpha23 [262, 3] (w:1, o:254, a:1, s:1, b:1),
% 2.38/2.72 alpha24 [263, 2] (w:1, o:233, a:1, s:1, b:1),
% 2.38/2.72 alpha25 [264, 2] (w:1, o:234, a:1, s:1, b:1),
% 2.38/2.72 alpha26 [265, 3] (w:1, o:255, a:1, s:1, b:1),
% 2.38/2.72 alpha27 [266, 3] (w:1, o:256, a:1, s:1, b:1),
% 2.38/2.72 alpha28 [267, 4] (w:1, o:289, a:1, s:1, b:1),
% 2.38/2.72 alpha29 [268, 3] (w:1, o:257, a:1, s:1, b:1),
% 2.38/2.72 alpha30 [269, 3] (w:1, o:259, a:1, s:1, b:1),
% 2.38/2.72 alpha31 [270, 4] (w:1, o:290, a:1, s:1, b:1),
% 2.38/2.72 alpha32 [271, 4] (w:1, o:291, a:1, s:1, b:1),
% 2.38/2.72 alpha33 [272, 3] (w:1, o:260, a:1, s:1, b:1),
% 2.38/2.72 alpha34 [273, 3] (w:1, o:261, a:1, s:1, b:1),
% 2.38/2.72 alpha35 [274, 3] (w:1, o:262, a:1, s:1, b:1),
% 2.38/2.72 alpha36 [275, 3] (w:1, o:263, a:1, s:1, b:1),
% 2.38/2.72 alpha37 [276, 3] (w:1, o:264, a:1, s:1, b:1),
% 2.38/2.72 alpha38 [277, 4] (w:1, o:292, a:1, s:1, b:1),
% 2.38/2.72 alpha39 [278, 4] (w:1, o:293, a:1, s:1, b:1),
% 2.38/2.72 alpha40 [279, 4] (w:1, o:294, a:1, s:1, b:1),
% 2.38/2.72 alpha41 [280, 4] (w:1, o:295, a:1, s:1, b:1),
% 2.38/2.72 alpha42 [281, 4] (w:1, o:296, a:1, s:1, b:1),
% 19.32/19.70 alpha43 [282, 4] (w:1, o:297, a:1, s:1, b:1),
% 19.32/19.70 alpha44 [283, 4] (w:1, o:298, a:1, s:1, b:1),
% 19.32/19.70 alpha45 [284, 3] (w:1, o:266, a:1, s:1, b:1),
% 19.32/19.70 alpha46 [285, 4] (w:1, o:299, a:1, s:1, b:1),
% 19.32/19.70 alpha47 [286, 4] (w:1, o:300, a:1, s:1, b:1),
% 19.32/19.70 alpha48 [287, 4] (w:1, o:301, a:1, s:1, b:1),
% 19.32/19.70 alpha49 [288, 4] (w:1, o:302, a:1, s:1, b:1),
% 19.32/19.70 alpha50 [289, 4] (w:1, o:303, a:1, s:1, b:1),
% 19.32/19.70 alpha51 [290, 4] (w:1, o:304, a:1, s:1, b:1),
% 19.32/19.70 alpha52 [291, 4] (w:1, o:305, a:1, s:1, b:1),
% 19.32/19.70 alpha53 [292, 4] (w:1, o:306, a:1, s:1, b:1),
% 19.32/19.70 alpha54 [293, 4] (w:1, o:307, a:1, s:1, b:1),
% 19.32/19.70 alpha55 [294, 4] (w:1, o:308, a:1, s:1, b:1),
% 19.32/19.70 alpha56 [295, 4] (w:1, o:309, a:1, s:1, b:1),
% 19.32/19.70 alpha57 [296, 4] (w:1, o:310, a:1, s:1, b:1),
% 19.32/19.70 alpha58 [297, 3] (w:1, o:268, a:1, s:1, b:1),
% 19.32/19.70 alpha59 [298, 3] (w:1, o:269, a:1, s:1, b:1),
% 19.32/19.70 alpha60 [299, 3] (w:1, o:271, a:1, s:1, b:1),
% 19.32/19.70 alpha61 [300, 4] (w:1, o:311, a:1, s:1, b:1),
% 19.32/19.70 alpha62 [301, 4] (w:1, o:312, a:1, s:1, b:1),
% 19.32/19.70 alpha63 [302, 4] (w:1, o:313, a:1, s:1, b:1),
% 19.32/19.70 skol1 [303, 2] (w:1, o:218, a:1, s:1, b:1),
% 19.32/19.70 skol2 [304, 2] (w:1, o:221, a:1, s:1, b:1),
% 19.32/19.70 skol3 [305, 2] (w:1, o:222, a:1, s:1, b:1),
% 19.32/19.70 skol4 [306, 3] (w:1, o:280, a:1, s:1, b:1),
% 19.32/19.70 skol5 [307, 2] (w:1, o:223, a:1, s:1, b:1),
% 19.32/19.70 skol6 [308, 3] (w:1, o:281, a:1, s:1, b:1),
% 19.32/19.70 skol7 [309, 3] (w:1, o:282, a:1, s:1, b:1),
% 19.32/19.70 skol8 [310, 3] (w:1, o:283, a:1, s:1, b:1),
% 19.32/19.70 skol9 [311, 3] (w:1, o:284, a:1, s:1, b:1),
% 19.32/19.70 skol10 [312, 2] (w:1, o:219, a:1, s:1, b:1),
% 19.32/19.70 skol11 [313, 1] (w:1, o:113, a:1, s:1, b:1),
% 19.32/19.70 skol12 [314, 2] (w:1, o:220, a:1, s:1, b:1),
% 19.32/19.70 skol13 [315, 4] (w:1, o:314, a:1, s:1, b:1),
% 19.32/19.70 skol14 [316, 3] (w:1, o:285, a:1, s:1, b:1).
% 19.32/19.70
% 19.32/19.70
% 19.32/19.70 Starting Search:
% 19.32/19.70
% 19.32/19.70 *** allocated 113905 integers for clauses
% 19.32/19.70 *** allocated 170857 integers for clauses
% 19.32/19.70 Resimplifying inuse:
% 19.32/19.70 Done
% 19.32/19.70
% 19.32/19.70
% 19.32/19.70 Intermediate Status:
% 19.32/19.70 Generated: 3034
% 19.32/19.70 Kept: 2045
% 19.32/19.71 Inuse: 36
% 19.32/19.71 Deleted: 0
% 19.32/19.71 Deletedinuse: 0
% 19.32/19.71
% 19.32/19.71 *** allocated 256285 integers for clauses
% 19.32/19.71 *** allocated 170857 integers for termspace/termends
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71
% 19.32/19.71 Intermediate Status:
% 19.32/19.71 Generated: 8566
% 19.32/19.71 Kept: 4198
% 19.32/19.71 Inuse: 133
% 19.32/19.71 Deleted: 3
% 19.32/19.71 Deletedinuse: 0
% 19.32/19.71
% 19.32/19.71 *** allocated 384427 integers for clauses
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71 *** allocated 256285 integers for termspace/termends
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71
% 19.32/19.71 Intermediate Status:
% 19.32/19.71 Generated: 13137
% 19.32/19.71 Kept: 6248
% 19.32/19.71 Inuse: 208
% 19.32/19.71 Deleted: 13
% 19.32/19.71 Deletedinuse: 0
% 19.32/19.71
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71 *** allocated 576640 integers for clauses
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71
% 19.32/19.71 Intermediate Status:
% 19.32/19.71 Generated: 16769
% 19.32/19.71 Kept: 8271
% 19.32/19.71 Inuse: 252
% 19.32/19.71 Deleted: 17
% 19.32/19.71 Deletedinuse: 0
% 19.32/19.71
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71
% 19.32/19.71 Intermediate Status:
% 19.32/19.71 Generated: 22712
% 19.32/19.71 Kept: 10334
% 19.32/19.71 Inuse: 293
% 19.32/19.71 Deleted: 18
% 19.32/19.71 Deletedinuse: 0
% 19.32/19.71
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71 *** allocated 384427 integers for termspace/termends
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71 *** allocated 864960 integers for clauses
% 19.32/19.71
% 19.32/19.71 Intermediate Status:
% 19.32/19.71 Generated: 28806
% 19.32/19.71 Kept: 12357
% 19.32/19.71 Inuse: 335
% 19.32/19.71 Deleted: 20
% 19.32/19.71 Deletedinuse: 0
% 19.32/19.71
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71
% 19.32/19.71 Intermediate Status:
% 19.32/19.71 Generated: 36427
% 19.32/19.71 Kept: 14925
% 19.32/19.71 Inuse: 356
% 19.32/19.71 Deleted: 20
% 19.32/19.71 Deletedinuse: 0
% 19.32/19.71
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71
% 19.32/19.71 Intermediate Status:
% 19.32/19.71 Generated: 40142
% 19.32/19.71 Kept: 16969
% 19.32/19.71 Inuse: 375
% 19.32/19.71 Deleted: 21
% 19.32/19.71 Deletedinuse: 0
% 19.32/19.71
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71 *** allocated 576640 integers for termspace/termends
% 19.32/19.71
% 19.32/19.71 Intermediate Status:
% 19.32/19.71 Generated: 45746
% 19.32/19.71 Kept: 18974
% 19.32/19.71 Inuse: 406
% 19.32/19.71 Deleted: 21
% 19.32/19.71 Deletedinuse: 0
% 19.32/19.71
% 19.32/19.71 *** allocated 1297440 integers for clauses
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71 Resimplifying clauses:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71
% 19.32/19.71 Intermediate Status:
% 19.32/19.71 Generated: 50903
% 19.32/19.71 Kept: 21123
% 19.32/19.71 Inuse: 445
% 19.32/19.71 Deleted: 189
% 19.32/19.71 Deletedinuse: 0
% 19.32/19.71
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71 Resimplifying inuse:
% 19.32/19.71 Done
% 19.32/19.71
% 19.32/19.71
% 19.32/19.71 Intermediate Status:
% 19.32/19.71 Generated: 55940
% 66.26/66.70 Kept: 23166
% 66.26/66.70 Inuse: 474
% 66.26/66.70 Deleted: 189
% 66.26/66.70 Deletedinuse: 0
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 62866
% 66.26/66.70 Kept: 25241
% 66.26/66.70 Inuse: 495
% 66.26/66.70 Deleted: 190
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 *** allocated 864960 integers for termspace/termends
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 72099
% 66.26/66.70 Kept: 27705
% 66.26/66.70 Inuse: 525
% 66.26/66.70 Deleted: 190
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 *** allocated 1946160 integers for clauses
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 80799
% 66.26/66.70 Kept: 30437
% 66.26/66.70 Inuse: 550
% 66.26/66.70 Deleted: 190
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 103006
% 66.26/66.70 Kept: 33824
% 66.26/66.70 Inuse: 575
% 66.26/66.70 Deleted: 190
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 111885
% 66.26/66.70 Kept: 35893
% 66.26/66.70 Inuse: 590
% 66.26/66.70 Deleted: 190
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 *** allocated 1297440 integers for termspace/termends
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 119792
% 66.26/66.70 Kept: 38904
% 66.26/66.70 Inuse: 635
% 66.26/66.70 Deleted: 190
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying clauses:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 125728
% 66.26/66.70 Kept: 40904
% 66.26/66.70 Inuse: 669
% 66.26/66.70 Deleted: 286
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 *** allocated 2919240 integers for clauses
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 134394
% 66.26/66.70 Kept: 42910
% 66.26/66.70 Inuse: 725
% 66.26/66.70 Deleted: 286
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 141730
% 66.26/66.70 Kept: 44940
% 66.26/66.70 Inuse: 768
% 66.26/66.70 Deleted: 286
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 148622
% 66.26/66.70 Kept: 47085
% 66.26/66.70 Inuse: 775
% 66.26/66.70 Deleted: 286
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 170615
% 66.26/66.70 Kept: 49402
% 66.26/66.70 Inuse: 785
% 66.26/66.70 Deleted: 286
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 178684
% 66.26/66.70 Kept: 51410
% 66.26/66.70 Inuse: 808
% 66.26/66.70 Deleted: 286
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 *** allocated 1946160 integers for termspace/termends
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 189099
% 66.26/66.70 Kept: 53433
% 66.26/66.70 Inuse: 833
% 66.26/66.70 Deleted: 286
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 198262
% 66.26/66.70 Kept: 56315
% 66.26/66.70 Inuse: 860
% 66.26/66.70 Deleted: 286
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 205837
% 66.26/66.70 Kept: 58439
% 66.26/66.70 Inuse: 880
% 66.26/66.70 Deleted: 286
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying clauses:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 223177
% 66.26/66.70 Kept: 60655
% 66.26/66.70 Inuse: 890
% 66.26/66.70 Deleted: 392
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 237570
% 66.26/66.70 Kept: 62892
% 66.26/66.70 Inuse: 915
% 66.26/66.70 Deleted: 392
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 247435
% 66.26/66.70 Kept: 65218
% 66.26/66.70 Inuse: 940
% 66.26/66.70 Deleted: 392
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 *** allocated 4378860 integers for clauses
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 269424
% 66.26/66.70 Kept: 67483
% 66.26/66.70 Inuse: 950
% 66.26/66.70 Deleted: 392
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 292426
% 66.26/66.70 Kept: 69753
% 66.26/66.70 Inuse: 960
% 66.26/66.70 Deleted: 392
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 309568
% 66.26/66.70 Kept: 71935
% 66.26/66.70 Inuse: 970
% 66.26/66.70 Deleted: 392
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 *** allocated 2919240 integers for termspace/termends
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 323904
% 66.26/66.70 Kept: 74110
% 66.26/66.70 Inuse: 990
% 66.26/66.70 Deleted: 392
% 66.26/66.70 Deletedinuse: 1
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70 Resimplifying inuse:
% 66.26/66.70 Done
% 66.26/66.70
% 66.26/66.70
% 66.26/66.70 Intermediate Status:
% 66.26/66.70 Generated: 333432
% 140.82/141.23 Kept: 76230
% 140.82/141.23 Inuse: 1015
% 140.82/141.23 Deleted: 392
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 342721
% 140.82/141.23 Kept: 78526
% 140.82/141.23 Inuse: 1040
% 140.82/141.23 Deleted: 392
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 364548
% 140.82/141.23 Kept: 81621
% 140.82/141.23 Inuse: 1060
% 140.82/141.23 Deleted: 392
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying clauses:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 387066
% 140.82/141.23 Kept: 84582
% 140.82/141.23 Inuse: 1075
% 140.82/141.23 Deleted: 845
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 395416
% 140.82/141.23 Kept: 86810
% 140.82/141.23 Inuse: 1100
% 140.82/141.23 Deleted: 845
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 403020
% 140.82/141.23 Kept: 88980
% 140.82/141.23 Inuse: 1138
% 140.82/141.23 Deleted: 847
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 410411
% 140.82/141.23 Kept: 91050
% 140.82/141.23 Inuse: 1173
% 140.82/141.23 Deleted: 847
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 420552
% 140.82/141.23 Kept: 93406
% 140.82/141.23 Inuse: 1193
% 140.82/141.23 Deleted: 847
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 430181
% 140.82/141.23 Kept: 95515
% 140.82/141.23 Inuse: 1218
% 140.82/141.23 Deleted: 847
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 443901
% 140.82/141.23 Kept: 98169
% 140.82/141.23 Inuse: 1238
% 140.82/141.23 Deleted: 847
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 453501
% 140.82/141.23 Kept: 100287
% 140.82/141.23 Inuse: 1273
% 140.82/141.23 Deleted: 847
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 463115
% 140.82/141.23 Kept: 102422
% 140.82/141.23 Inuse: 1288
% 140.82/141.23 Deleted: 847
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying clauses:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 *** allocated 6568290 integers for clauses
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 *** allocated 4378860 integers for termspace/termends
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 476817
% 140.82/141.23 Kept: 105563
% 140.82/141.23 Inuse: 1303
% 140.82/141.23 Deleted: 986
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 490286
% 140.82/141.23 Kept: 107815
% 140.82/141.23 Inuse: 1318
% 140.82/141.23 Deleted: 986
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 500616
% 140.82/141.23 Kept: 109830
% 140.82/141.23 Inuse: 1352
% 140.82/141.23 Deleted: 986
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 513707
% 140.82/141.23 Kept: 111855
% 140.82/141.23 Inuse: 1371
% 140.82/141.23 Deleted: 986
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 521596
% 140.82/141.23 Kept: 114058
% 140.82/141.23 Inuse: 1383
% 140.82/141.23 Deleted: 986
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 531202
% 140.82/141.23 Kept: 116067
% 140.82/141.23 Inuse: 1414
% 140.82/141.23 Deleted: 986
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 541605
% 140.82/141.23 Kept: 118070
% 140.82/141.23 Inuse: 1424
% 140.82/141.23 Deleted: 986
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 554315
% 140.82/141.23 Kept: 121293
% 140.82/141.23 Inuse: 1428
% 140.82/141.23 Deleted: 986
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 565756
% 140.82/141.23 Kept: 124888
% 140.82/141.23 Inuse: 1438
% 140.82/141.23 Deleted: 986
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying clauses:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 582049
% 140.82/141.23 Kept: 128768
% 140.82/141.23 Inuse: 1453
% 140.82/141.23 Deleted: 1177
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 601815
% 140.82/141.23 Kept: 132522
% 140.82/141.23 Inuse: 1473
% 140.82/141.23 Deleted: 1177
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 619769
% 140.82/141.23 Kept: 135603
% 140.82/141.23 Inuse: 1483
% 140.82/141.23 Deleted: 1177
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 140.82/141.23 Generated: 633504
% 140.82/141.23 Kept: 140979
% 140.82/141.23 Inuse: 1503
% 140.82/141.23 Deleted: 1177
% 140.82/141.23 Deletedinuse: 1
% 140.82/141.23
% 140.82/141.23 Resimplifying inuse:
% 140.82/141.23 Done
% 140.82/141.23
% 140.82/141.23
% 140.82/141.23 Intermediate Status:
% 241.74/242.19 Generated: 642719
% 241.74/242.19 Kept: 145303
% 241.74/242.19 Inuse: 1513
% 241.74/242.19 Deleted: 1177
% 241.74/242.19 Deletedinuse: 1
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying clauses:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 650293
% 241.74/242.19 Kept: 147305
% 241.74/242.19 Inuse: 1538
% 241.74/242.19 Deleted: 1188
% 241.74/242.19 Deletedinuse: 1
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 *** allocated 9852435 integers for clauses
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 689714
% 241.74/242.19 Kept: 152965
% 241.74/242.19 Inuse: 1568
% 241.74/242.19 Deleted: 1188
% 241.74/242.19 Deletedinuse: 1
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 700702
% 241.74/242.19 Kept: 155043
% 241.74/242.19 Inuse: 1588
% 241.74/242.19 Deleted: 1188
% 241.74/242.19 Deletedinuse: 1
% 241.74/242.19
% 241.74/242.19 *** allocated 6568290 integers for termspace/termends
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 708495
% 241.74/242.19 Kept: 157147
% 241.74/242.19 Inuse: 1618
% 241.74/242.19 Deleted: 1188
% 241.74/242.19 Deletedinuse: 1
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 717644
% 241.74/242.19 Kept: 159505
% 241.74/242.19 Inuse: 1637
% 241.74/242.19 Deleted: 1189
% 241.74/242.19 Deletedinuse: 1
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 729657
% 241.74/242.19 Kept: 162956
% 241.74/242.19 Inuse: 1657
% 241.74/242.19 Deleted: 1189
% 241.74/242.19 Deletedinuse: 1
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 737190
% 241.74/242.19 Kept: 165602
% 241.74/242.19 Inuse: 1662
% 241.74/242.19 Deleted: 1189
% 241.74/242.19 Deletedinuse: 1
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying clauses:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 747153
% 241.74/242.19 Kept: 167767
% 241.74/242.19 Inuse: 1692
% 241.74/242.19 Deleted: 2751
% 241.74/242.19 Deletedinuse: 1
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 754808
% 241.74/242.19 Kept: 169869
% 241.74/242.19 Inuse: 1717
% 241.74/242.19 Deleted: 2751
% 241.74/242.19 Deletedinuse: 1
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 764226
% 241.74/242.19 Kept: 172513
% 241.74/242.19 Inuse: 1727
% 241.74/242.19 Deleted: 2751
% 241.74/242.19 Deletedinuse: 1
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 783222
% 241.74/242.19 Kept: 175306
% 241.74/242.19 Inuse: 1744
% 241.74/242.19 Deleted: 2754
% 241.74/242.19 Deletedinuse: 1
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 792553
% 241.74/242.19 Kept: 177412
% 241.74/242.19 Inuse: 1769
% 241.74/242.19 Deleted: 2755
% 241.74/242.19 Deletedinuse: 2
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 800250
% 241.74/242.19 Kept: 179419
% 241.74/242.19 Inuse: 1782
% 241.74/242.19 Deleted: 2755
% 241.74/242.19 Deletedinuse: 2
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 809027
% 241.74/242.19 Kept: 181440
% 241.74/242.19 Inuse: 1803
% 241.74/242.19 Deleted: 2755
% 241.74/242.19 Deletedinuse: 2
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 836985
% 241.74/242.19 Kept: 185075
% 241.74/242.19 Inuse: 1814
% 241.74/242.19 Deleted: 2755
% 241.74/242.19 Deletedinuse: 2
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying clauses:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 846906
% 241.74/242.19 Kept: 187093
% 241.74/242.19 Inuse: 1830
% 241.74/242.19 Deleted: 3137
% 241.74/242.19 Deletedinuse: 2
% 241.74/242.19
% 241.74/242.19 Resimplifying inuse:
% 241.74/242.19 Done
% 241.74/242.19
% 241.74/242.19
% 241.74/242.19 Intermediate Status:
% 241.74/242.19 Generated: 862878
% 241.74/242.19 Kept: 190135
% 241.74/242.19 Inuse: 1834
% 241.74/242.19 Deleted: 3137
% 241.74/242.19 Deletedinuse: 2
% 241.74/242.20
% 241.74/242.20 Resimplifying inuse:
% 241.74/242.20 Done
% 241.74/242.20
% 241.74/242.20 Resimplifying inuse:
% 241.74/242.20 Done
% 241.74/242.20
% 241.74/242.20
% 241.74/242.20 Intermediate Status:
% 241.74/242.20 Generated: 873110
% 241.74/242.20 Kept: 192170
% 241.74/242.20 Inuse: 1844
% 241.74/242.20 Deleted: 3137
% 241.74/242.20 Deletedinuse: 2
% 241.74/242.20
% 241.74/242.20 Resimplifying inuse:
% 241.74/242.20 Done
% 241.74/242.20
% 241.74/242.20 Resimplifying inuse:
% 241.74/242.20 Done
% 241.74/242.20
% 241.74/242.20
% 241.74/242.20 Intermediate Status:
% 241.74/242.20 Generated: 881101
% 241.74/242.20 Kept: 194184
% 241.74/242.20 Inuse: 1855
% 241.74/242.20 Deleted: 3137
% 241.74/242.20 Deletedinuse: 2
% 241.74/242.20
% 241.74/242.20 Resimplifying inuse:
% 241.74/242.20 Done
% 241.74/242.20
% 241.74/242.20
% 241.74/242.20 Intermediate Status:
% 241.74/242.20 Generated: 890797
% 241.74/242.20 Kept: 196362
% 241.74/242.20 Inuse: 1859
% 241.74/242.20 Deleted: 3137
% 241.74/242.20 Deletedinuse: 2
% 241.74/242.20
% 241.74/242.20 Resimplifying inuse:
% 241.74/242.20 Done
% 241.74/242.20
% 241.74/242.20 Resimplifying inuse:
% 241.74/242.20 Done
% 241.74/242.20
% 241.74/242.20
% 241.74/242.20 Intermediate Status:
% 241.74/242.20 Generated: 900479
% 241.74/242.20 Kept: 198595
% 241.74/242.20 Inuse: 1869
% 241.74/242.20 Deleted: 3137
% 241.74/242.20 Deletedinuse: 2
% 241.74/242.20
% 241.74/242.20 Resimplifying inuse:
% 241.74/242.20 Done
% 241.74/242.20
% 241.74/242.20 Resimplifying inuse:
% 241.74/242.20 Done
% 241.74/242.20
% 241.74/242.20
% 241.74/242.20 Intermediate Status:
% 241.74/242.20 Generated: 930957
% 241.74/242.20 Kept: 200720
% 241.74/242.20 Inuse: 1889
% 241.74/242.20 Deleted: 3137
% 241.74/242.20 Deletedinuse: 2
% 241.74/242.20
% 241.74/242.20 Resimplifying inuse:
% 241.74/242.20 Done
% 241.74/242.20
% 241.74/242.20 Resimplifying inuse:
% 241.74/242.20 Done
% 241.74/242.20
% 241.74/242.20
% 241.74/242.20 Intermediate Status:
% 241.74/242.20 Generated: 948132
% 241.74/242.20 Kept: 204150
% 241.74/242.20 Inuse: 1899
% 241.74/242.20 Deleted: 3137
% 241.74/242.20 Deletedinuse: 2
% 241.74/242.20
% 241.74/242.20 ResimplCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------