TSTP Solution File: SWW218+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW218+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:19 EDT 2022
% Result : Timeout 300.07s 300.58s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW218+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n020.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 : Sun Jun 5 00:45:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.95/1.62 *** allocated 10000 integers for termspace/termends
% 0.95/1.62 *** allocated 10000 integers for clauses
% 0.95/1.62 *** allocated 10000 integers for justifications
% 0.95/1.62 *** allocated 15000 integers for termspace/termends
% 0.95/1.62 *** allocated 22500 integers for termspace/termends
% 0.95/1.62 *** allocated 33750 integers for termspace/termends
% 0.95/1.62 Bliksem 1.12
% 0.95/1.62
% 0.95/1.62
% 0.95/1.62 Automatic Strategy Selection
% 0.95/1.62
% 0.95/1.62 *** allocated 50625 integers for termspace/termends
% 0.95/1.62 *** allocated 75937 integers for termspace/termends
% 0.95/1.62 *** allocated 113905 integers for termspace/termends
% 0.95/1.62
% 0.95/1.62 Clauses:
% 0.95/1.62
% 0.95/1.62 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_r ) }.
% 0.95/1.62 { ! alpha1( Y ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y )
% 0.95/1.62 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, skol2 ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, skol2 ), alpha1(
% 0.95/1.62 skol56( Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, skol2 ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, skol56( X ) ) }.
% 0.95/1.62 { ! alpha1( X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, skol3( Y ) ), v_r )
% 0.95/1.62 }.
% 0.95/1.62 { ! alpha1( X ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP
% 0.95/1.62 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol3( X ) ) ) =
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ), v_r ), !
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.95/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), Y ) ) =
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), alpha1( X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ), v_r ), !
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.95/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), Y ) ) =
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, skol4 ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), v_r ), !
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.95/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) ) =
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), v_r ) }.
% 0.95/1.62 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.95/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) =
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.95/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, skol5 ), v_r ) }.
% 0.95/1.62 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.95/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol5 ) ) =
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, skol57 ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.95/1.62 , Y ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.62 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.95/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_r ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), v_r ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.95/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol6 ) ),
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.95/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.62 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.62 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.62 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.95/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.62 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.95/1.62 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.95/1.62 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.62 = Y }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( X ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Y ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 = Y }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.62 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.95/1.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, Y ), Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.62 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 , Y ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.62 , Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.62 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_RealDef_Oreal ) ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.62 hAPP( Y, U ) ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.95/1.62 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.95/1.62 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.62 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.62 hAPP( Y, U ) ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.62 ( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.62 ( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.62 hAPP( Y, U ) ) }.
% 0.95/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.95/1.62 ( Z, skol7( X, Y, Z ) ), hAPP( Y, skol7( X, Y, Z ) ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.62 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.62 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.95/1.62 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.95/1.62 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.95/1.62 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.62 , ! Y = Z }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.62 , ! Z = Y }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.62 , ! Z = Y }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.62 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.62 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.62 Y ), ! Z = Y }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.62 Z ), ! Z = Y }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.62 Y ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.62 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.62 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.62 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.95/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.95/1.62 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.95/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.95/1.62 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.62 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.62 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.62 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.62 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.62 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.62 ( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.62 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.62 , ! Z = Y }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.62 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.62 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.95/1.62 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.62 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.95/1.62 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, Y ), Z ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.62 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, Z ), Y ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.62 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__semidom( X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol8( Z, T ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.95/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol8( X, Y ) ) }.
% 0.95/1.62 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_RealDef_Oreal ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_RealDef_Oreal ) }.
% 0.95/1.62 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.62 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.62 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.95/1.62 ( X ) ) ) }.
% 0.95/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.95/1.62 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.95/1.63 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.95/1.63 }.
% 0.95/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.63 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.95/1.63 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.95/1.63 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.95/1.63 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.63 }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.63 }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.95/1.63 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.95/1.63 ) }.
% 0.95/1.63 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.95/1.63 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.95/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.95/1.63 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.95/1.63 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.63 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.95/1.63 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.95/1.63 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.95/1.63 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.95/1.63 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.95/1.63 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.63 }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.95/1.63 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.63 }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.63 X, Y, Z ) }.
% 0.95/1.63 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.63 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.95/1.63 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.95/1.63 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.95/1.63 ) ) }.
% 0.95/1.63 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.95/1.63 ( X, Y ), Z = Y }.
% 0.95/1.63 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.95/1.63 ( X, Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.95/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.63 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.95/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.63 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.95/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.63 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), !
% 0.95/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.95/1.63 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.63 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.95/1.63 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.95/1.63 { c_RealDef_Opositive( X ), X = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_RealDef_Oreal ), c_RealDef_Opositive( c_Groups_Ouminus__class_Ouminus
% 0.95/1.63 ( tc_RealDef_Oreal, X ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol9( Z, T ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol9( X, Y ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol58( X, Y, Z ) ) ), Z ),
% 0.95/1.63 c_SEQ_OBseq( X, Y ) }.
% 0.95/1.63 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.95/1.63 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.63 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ) ) = Z }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.95/1.63 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.95/1.63 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.95/1.63 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.95/1.63 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.95/1.63 c_Polynomial_Ocoeff( X, Y ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.95/1.63 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol10( X
% 0.95/1.63 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol10( X, Y, Z ) ), Z =
% 0.95/1.63 Y }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.95/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.95/1.63 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.95/1.63 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.95/1.63 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.95/1.63 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.95/1.63 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha2
% 0.95/1.63 ( X, Y, Z ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.63 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! alpha2( X, Y, Z ),
% 0.95/1.63 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.95/1.63 { ! alpha2( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.95/1.63 ( X ) ) }.
% 0.95/1.63 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.63 alpha2( X, Y, Z ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.63 { ! c_RealDef_Opositive( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.95/1.63 }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.95/1.63 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.95/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.95/1.63 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.95/1.63 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.95/1.63 ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol11( X, Y, Z ) ) ), Y ),
% 0.95/1.63 c_SEQ_OBseq( X, Z ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol12( Z, T ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol12( X, Y ) ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons
% 0.95/1.63 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.95/1.63 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X, Z,
% 0.95/1.63 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ),
% 0.95/1.63 hAPP( c_Polynomial_Opoly( X, Y ), c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.95/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.95/1.63 ) ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.95/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.95/1.63 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.95/1.63 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.95/1.63 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 0.95/1.63 }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.95/1.63 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.95/1.63 { alpha27( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.95/1.63 ( X, Y ), Z ) ) }.
% 0.95/1.63 { ! alpha27( X, Y, Z ), alpha30( X, Y, Z ), Z = Y }.
% 0.95/1.63 { ! alpha27( X, Y, Z ), alpha30( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.95/1.63 ) ) }.
% 0.95/1.63 { ! alpha30( X, Y, Z ), alpha27( X, Y, Z ) }.
% 0.95/1.63 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha27( X, Y, Z ) }.
% 0.95/1.63 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.95/1.63 }.
% 0.95/1.63 { ! alpha30( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.95/1.63 X, Y ), Z ) ), alpha30( X, Y, Z ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.95/1.63 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.95/1.63 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.95/1.63 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 0.95/1.63 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.63 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.63 ) ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.95/1.63 , Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.95/1.63 , Y ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.95/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.95/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.95/1.63 .
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.95/1.63 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_Nat_Onat, skol13( X, Y ), skol59( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.95/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.63 hAPP( Y, skol59( X, Y ) ), hAPP( Y, skol13( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.95/1.63 , Y ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 0.95/1.63 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_Nat_Onat, skol14( X, Y ), skol60( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.95/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.63 hAPP( Y, skol14( X, Y ) ), hAPP( Y, skol60( X, Y ) ) ), c_SEQ_Oincseq( X
% 0.95/1.63 , Y ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol15( U, W, V0, T )
% 0.95/1.63 ), c_SEQ_OBseq( X, Y ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol15( X, Y, Z, T ) ) ), Z
% 0.95/1.63 ), c_SEQ_OBseq( X, Y ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 0.95/1.63 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 0.95/1.63 , Y ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.95/1.63 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.95/1.63 ( X ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X
% 0.95/1.63 , Z, Y ) ) = c_Nat_Onat_Onat__case( X, Z, c_Polynomial_Ocoeff( X, Y ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.95/1.63 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.95/1.63 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.95/1.63 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.95/1.63 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.95/1.63 c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.95/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 0.95/1.63 c_Polynomial_Odegree( X, Z ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.95/1.63 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.95/1.63 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X
% 0.95/1.63 ) ) }.
% 0.95/1.63 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ) ) = Y }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.95/1.63 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.63 c_Polynomial_Odegree( X, Y ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL
% 0.95/1.63 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Y ),
% 0.95/1.63 Z ) ), Z = Y }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.95/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.95/1.63 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), Z ), Y ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.95/1.63 }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.95/1.63 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.63 }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.95/1.63 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.63 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.63 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), hBOOL( hAPP
% 0.95/1.63 ( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.95/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.95/1.63 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.95/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.95/1.63 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.95/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.95/1.63 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.95/1.63 ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.63 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.95/1.63 ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.95/1.63 ), Z ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.95/1.63 Z ), Y ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , ! X = Y }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , ! Y = X }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , ! Y = X }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.95/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.95/1.63 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.95/1.63 ) ) }.
% 0.95/1.63 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.95/1.63 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.95/1.63 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.95/1.63 ), Z ) ) }.
% 0.95/1.63 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.95/1.63 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.95/1.63 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.95/1.63 Z ), Y ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.95/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.63 ), Y = X }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.63 ), Y = X }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.95/1.63 ), Z ) ) }.
% 0.95/1.63 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.95/1.63 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.95/1.63 ), Z ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.63 , X ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.95/1.63 ), Y ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , Y = X }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.63 ), Y = X }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.63 ), X = Y }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.95/1.63 ), Y ) ) }.
% 0.95/1.63 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.63 , X ) ) }.
% 0.95/1.63 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.63 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.63 , X ) ) }.
% 0.95/1.63 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.63 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.95/1.63 ), Y ) ) }.
% 0.95/1.63 { ! alpha3( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.63 { ! alpha3( X, Y ), ! Y = X }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , Y = X, alpha3( X, Y ) }.
% 0.95/1.63 { ! alpha3( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.63 { ! alpha3( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , alpha3( X, Y ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , alpha4( X, Y ), Y = X }.
% 0.95/1.63 { ! alpha4( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.63 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.63 , X ) ) }.
% 0.95/1.63 { ! alpha4( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.63 { ! alpha4( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.95/1.63 , alpha4( X, Y ) }.
% 0.95/1.63 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.95/1.63 , X ) ) }.
% 0.95/1.63 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 0.95/1.63 , Y ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.95/1.63 ), Y = X }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.63 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Nat_Onat ) ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.95/1.63 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.95/1.63 ), X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.95/1.63 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.95/1.63 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.95/1.63 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.95/1.63 ) }.
% 0.95/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Nat_Onat ) ) = Y }.
% 0.95/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( X ) }.
% 0.95/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.63 = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.63 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 0.95/1.63 ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.63 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.63 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.95/1.63 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ) }.
% 0.95/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.63 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.95/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.95/1.63 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.63 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.63 X ), T ), Z ) ), Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.95/1.63 , U, Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), T ), U ) ), Y ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ), hBOOL( hAPP( hAPP
% 0.95/1.63 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.63 ( X ), Z ), U ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T
% 0.95/1.63 ) ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP
% 0.95/1.63 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.63 ( X ), T ), Z ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y
% 0.95/1.63 ) ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.95/1.63 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.63 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.95/1.63 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.95/1.63 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.95/1.63 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Nat_Onat ), Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.63 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.95/1.63 Y ) ) ) ), Y ) ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.63 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.95/1.63 Y ) ) ) ), Y ) ) }.
% 0.95/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.95/1.63 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.95/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.95/1.63 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.63 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.95/1.63 X ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 0.95/1.63 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.95/1.63 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.95/1.63 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.95/1.63 { ! c_Nat_OSuc( X ) = X }.
% 0.95/1.63 { ! X = c_Nat_OSuc( X ) }.
% 0.95/1.63 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.63 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.63 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.95/1.63 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.95/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.95/1.63 }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.95/1.63 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.95/1.63 X ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.95/1.63 .
% 0.95/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.95/1.63 .
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.95/1.63 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.95/1.63 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.95/1.63 .
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.95/1.63 ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.95/1.63 , c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.95/1.63 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.95/1.63 }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.95/1.63 c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.95/1.63 ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), c_Nat_OSuc( X ) ) = hAPP( Y, X )
% 0.95/1.63 }.
% 0.95/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.63 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha5( X, Y ) }.
% 0.95/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { ! alpha5( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.63 c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { ! alpha5( X, Y ), Y = c_Nat_OSuc( skol16( Z, Y ) ) }.
% 0.95/1.63 { ! alpha5( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol16( X,
% 0.95/1.63 Y ), X ) }.
% 0.95/1.63 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.95/1.63 ), alpha5( X, Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol17( X ) ) }.
% 0.95/1.63 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.95/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.95/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hBOOL(
% 0.95/1.63 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.95/1.63 .
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.63 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.95/1.63 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 X ), Y ), Z = Y }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.63 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.63 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.95/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.95/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.95/1.63 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.95/1.63 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 0.95/1.63 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.95/1.63 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 0.95/1.63 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.95/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Nat_Onat ) ) = Y }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.95/1.63 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.95/1.63 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.95/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.95/1.63 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.95/1.63 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.95/1.63 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.95/1.63 c_Polynomial_Odegree( X, Y ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.95/1.63 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ), Y ) }.
% 0.95/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.95/1.63 ), X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.95/1.63 , skol18( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Polynomial_Odegree( X, Y ), Z ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol18( X
% 0.95/1.63 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.95/1.63 Y ), Z ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.63 }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X, Z, Y ) =
% 0.95/1.63 c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 0.95/1.63 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Z ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Y ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.63 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.95/1.63 , T ), Z ) ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.63 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.95/1.63 , T ), Y ) ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.63 ( tc_Polynomial_Opoly( X ) ), T ), Z ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ), hBOOL(
% 0.95/1.63 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.63 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), T ) ), hBOOL(
% 0.95/1.63 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Y, T ) ) ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 0.95/1.63 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.63 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha31( X, Y, Z, T ), ! Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.95/1.63 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.95/1.63 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha31( X, Y, Z, T ), ! hAPP(
% 0.95/1.63 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.95/1.63 .
% 0.95/1.63 { ! alpha31( X, Y, Z, T ), alpha33( X, Y, Z, T ), alpha28( X, Y, T ) }.
% 0.95/1.63 { ! alpha31( X, Y, Z, T ), alpha33( X, Y, Z, T ), ! hAPP(
% 0.95/1.63 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! alpha33( X, Y, Z, T ), alpha31( X, Y, Z, T ) }.
% 0.95/1.63 { ! alpha28( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.95/1.63 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.63 alpha31( X, Y, Z, T ) }.
% 0.95/1.63 { ! alpha33( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), Z ), T ) ), alpha34( X, Y, Z, T ) }.
% 0.95/1.63 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 Z ), T ) ), alpha33( X, Y, Z, T ) }.
% 0.95/1.63 { ! alpha34( X, Y, Z, T ), alpha33( X, Y, Z, T ) }.
% 0.95/1.63 { ! alpha34( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), skol19( X, Y, U, W ) ), Y ) ) }.
% 0.95/1.63 { ! alpha34( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), skol19( X, Y, U, T ) ), T ) ) }.
% 0.95/1.63 { ! alpha34( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), skol19( X, Y, Z, T ) ), Z ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.95/1.63 , U ), Y ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), U ), Z ) ), alpha34
% 0.95/1.63 ( X, Y, Z, T ) }.
% 0.95/1.63 { ! alpha28( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! alpha28( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha28( X, Y, Z
% 0.95/1.63 ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 Z, c_Polynomial_Odegree( X, Y ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.63 tc_Nat_Onat, Z, skol20( T, U, Z ) ) }.
% 0.95/1.63 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 Z, c_Polynomial_Odegree( X, Y ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.63 skol20( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Omono( tc_Nat_Onat, X
% 0.95/1.63 , c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), T ), Z ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol21( X, Y, Z ) ) ), Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, c_Nat_OSuc( skol61( X, Y ) ) ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol69( X, Y, Z ) ) ),
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol73( T, U ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol69( X, Y, Z ) ) ),
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol73( X, Y ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol22( X, Y, Z ) ) ), Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, c_Nat_OSuc( skol62( X, Y ) ) ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol70( X, Y, Z ) ) ),
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol74( T, U ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol70( X, Y, Z ) ) ),
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol74( X, Y ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, X ) ) }.
% 0.95/1.63 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.95/1.63 Y = X }.
% 0.95/1.63 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.95/1.63 , X ) }.
% 0.95/1.63 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.63 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.63 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.95/1.63 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.95/1.63 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.95/1.63 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.63 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.63 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.95/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.95/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 0.95/1.63 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, X ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, c_Nat_OSuc( skol23( X, Y ) ) ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol63( X, Y, Z ) ) ),
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, c_Nat_OSuc( skol24( X, Y ) ) ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol64( X, Y, Z ) ) ),
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Orderings_Oorder( X ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), skol25( X, Y ) ), skol65( X, Y )
% 0.95/1.63 ) ), c_Orderings_Oorder_Omono( tc_Nat_Onat, X, c_Rings_Odvd__class_Odvd
% 0.95/1.63 ( tc_Nat_Onat ), Y ) }.
% 0.95/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.63 hAPP( Y, skol25( X, Y ) ), hAPP( Y, skol65( X, Y ) ) ),
% 0.95/1.63 c_Orderings_Oorder_Omono( tc_Nat_Onat, X, c_Rings_Odvd__class_Odvd(
% 0.95/1.63 tc_Nat_Onat ), Y ) }.
% 0.95/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.63 hAPP( Y, skol26( X, Y ) ), hAPP( Y, c_Nat_OSuc( skol26( X, Y ) ) ) ),
% 0.95/1.63 c_SEQ_Oincseq( X, Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, skol27( X ) ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, c_Nat_OSuc( skol27( X ) ) ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol28( Z, T ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol28( X, Y ) ), X ) =
% 0.95/1.63 Y }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( Z, T ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol29( X, Y ) ), X ) =
% 0.95/1.63 Y }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.95/1.63 skol29( X, Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_RComplete_Onatfloor( X ), Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.95/1.63 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.95/1.63 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.95/1.63 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_RComplete_Onatceiling( X ), Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol30( Z, T ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol30( X, Y ) ),
% 0.95/1.63 c_Nat_OSuc( Y ) ) = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.95/1.63 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.95/1.63 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.95/1.63 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.95/1.63 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.95/1.63 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.95/1.63 }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.95/1.63 ), c_RComplete_Onatfloor( X ) ) }.
% 0.95/1.63 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.63 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.95/1.63 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.95/1.63 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.95/1.63 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.95/1.63 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.95/1.63 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.95/1.63 , c_RComplete_Onatfloor( X ) ) }.
% 0.95/1.63 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.95/1.63 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.63 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.63 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.95/1.63 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.63 }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.95/1.63 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_RComplete_Onatceiling( Y ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.95/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.95/1.63 , c_RComplete_Onatfloor( X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.95/1.63 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.95/1.63 c_RComplete_Onatfloor( X ) = Y }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z )
% 0.95/1.63 , c_NthRoot_Oroot( Y, Z ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 0.95/1.63 Z ), c_NthRoot_Oroot( Y, Z ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.95/1.63 ), X ) = Y }.
% 0.95/1.63 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.95/1.63 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.95/1.63 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.95/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ) ) = X }.
% 0.95/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ), X ) = X }.
% 0.95/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.63 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.95/1.63 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.63 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.63 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.63 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.95/1.63 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.63 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.95/1.63 , X ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.95/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol31( X, Y ) ) }.
% 0.95/1.63 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.63 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.95/1.63 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.95/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.63 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.95/1.63 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.95/1.63 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.95/1.63 ( X, Y ) ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.95/1.63 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.95/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.95/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.95/1.63 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.95/1.63 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.95/1.63 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.95/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 T, Y ), Z = Y }.
% 0.95/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 T, Y ) }.
% 0.95/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 Y, Z ), T = Y }.
% 0.95/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 Y, Z ) }.
% 0.95/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 T, Y ), Z = Y }.
% 0.95/1.63 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 T, Y ), Z = Y }.
% 0.95/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 Y, T ), Z = Y }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.95/1.63 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.95/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.95/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.95/1.63 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.95/1.63 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.95/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.95/1.63 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, Y, T
% 0.95/1.63 ) ) ) }.
% 0.95/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 Z, Y ) ) = Y }.
% 0.95/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.63 Y ) ) = Y }.
% 0.95/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.95/1.63 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.95/1.63 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.63 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, Z, Y ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.95/1.63 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, Z, Y ) }.
% 0.95/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.63 , T ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.63 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.63 , T, Y ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.63 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.63 , Y, T ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.63 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, Z, Y ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.63 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.63 , T, Y ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, T, Y ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.63 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.63 , Y, Z ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.63 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.63 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.63 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.63 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.63 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.63 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.63 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.95/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.63 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.95/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.63 { c_NthRoot_Oroot( X, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.63 { ! c_RealDef_Opositive( X ), ! c_RealDef_Opositive( Y ),
% 0.95/1.63 c_RealDef_Opositive( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X, Y
% 0.95/1.63 ) ) }.
% 0.95/1.63 { c_NthRoot_Oroot( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.95/1.63 , X ) = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_NthRoot_Oroot( X, Z ) = c_NthRoot_Oroot( X, Y )
% 0.95/1.63 , Z = Y }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! Z = Y, c_NthRoot_Oroot( X, Z ) = c_NthRoot_Oroot
% 0.95/1.63 ( X, Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), c_NthRoot_Oroot( X,
% 0.95/1.63 c_NthRoot_Oroot( Y, Z ) ) = c_NthRoot_Oroot( Y, c_NthRoot_Oroot( X, Z ) )
% 0.95/1.63 }.
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.63 ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 Z, Y ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 Y, Z ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.95/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.63 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.95/1.63 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ) }.
% 0.95/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.63 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.63 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.63 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.63 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.63 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.63 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.63 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.63 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.95/1.63 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.63 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.95/1.63 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.95/1.63 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.63 , Y, T ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.63 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.63 Z ) = Y }.
% 0.95/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.63 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.95/1.63 ( X, Z ) }.
% 0.95/1.63 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.63 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.63 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.63 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.95/1.63 ( X, Y ) }.
% 0.95/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.95/1.63 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.95/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha6( X, Y ), alpha16( X
% 0.95/1.63 , Y ) }.
% 0.95/1.63 { ! alpha6( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! alpha16( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! alpha16( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! alpha16( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha16( X, Y ) }.
% 0.95/1.63 { ! alpha6( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! alpha6( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha6( X, Y ) }.
% 0.95/1.63 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha7( X, Y ), alpha17
% 0.95/1.63 ( X, Y ) }.
% 0.95/1.63 { ! alpha7( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.63 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! alpha17( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.63 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! alpha17( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! alpha17( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha17( X, Y ) }.
% 0.95/1.63 { ! alpha7( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! alpha7( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol32( X, Y ) ) ) }.
% 0.95/1.63 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.95/1.63 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.95/1.63 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.95/1.63 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.63 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.95/1.63 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.95/1.63 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.95/1.63 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.63 , Y ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, Z, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, Z, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_NthRoot_Oroot( X, Y ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.95/1.63 ), c_NthRoot_Oroot( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_RealDef_Oreal ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 Z, Y ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot
% 0.95/1.63 ( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 Z, Y ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot
% 0.95/1.63 ( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, hAPP( hAPP(
% 0.95/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), Y ) ) = hAPP( hAPP
% 0.95/1.63 ( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Z
% 0.95/1.63 ) ), Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_NthRoot_Oroot( X, Y ) =
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y =
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.95/1.63 , c_NthRoot_Oroot( X, Y ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.95/1.63 }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_RealDef_Oreal ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.63 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.63 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.63 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.63 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.63 ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.63 ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.63 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.63 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.63 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.63 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.63 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.63 ( tc_RealDef_Oreal, Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.95/1.63 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Nat_Onat ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_RealDef_Oreal ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.95/1.63 , Y, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, Y, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 0.95/1.63 Y ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.63 c_NthRoot_Oroot( X, Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ) }
% 0.95/1.63 .
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_NthRoot_Oroot( X, Y ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.95/1.63 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 Y, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 0.95/1.63 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.95/1.63 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( Y,
% 0.95/1.63 Z ), c_NthRoot_Oroot( X, Z ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y ), c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_RealDef_Oreal ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.95/1.63 , Y, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, Y, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 0.95/1.63 Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.95/1.63 c_NthRoot_Oroot( X, Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 0.95/1.63 }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.95/1.63 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( Y, Z )
% 0.95/1.63 , c_NthRoot_Oroot( X, Z ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_NthRoot_Oroot( X, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.95/1.63 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 Y, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 0.95/1.63 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 0.95/1.63 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 0.95/1.63 }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), c_NthRoot_Oroot(
% 0.95/1.63 c_Nat_OSuc( Y ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.63 tc_RealDef_Oreal ), X ), c_Nat_OSuc( Y ) ) ) = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.63 tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_RealDef_Oreal ) ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.95/1.63 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.95/1.63 , X ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_RealDef_Oreal ) ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 0.95/1.63 , c_NthRoot_Oroot( X, Z ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.95/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X ) =
% 0.95/1.63 Z, c_NthRoot_Oroot( X, Z ) = Y }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.95/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.95/1.63 c_NthRoot_Oroot( X, Y ) ), X ) = Y }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.95/1.63 c_NthRoot_Oroot( X, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.63 tc_RealDef_Oreal ), Y ), X ) ) = Y }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.63 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.95/1.63 ) ) }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.63 ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol33( Z, T ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.63 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, skol66( X, Y ) ) ) ),
% 0.95/1.63 skol33( X, Y ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.63 ( Y, skol71( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, T ) ) )
% 0.95/1.63 , Z ), c_SEQ_OBseq( X, Y ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol34( Z, T ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.63 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y, skol67( X, Y ) ) )
% 0.95/1.63 ) ), skol34( X, Y ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.63 ( Y, skol72( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y
% 0.95/1.63 , T ) ) ) ), Z ), c_SEQ_OBseq( X, Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol35( X, Y ) ) }.
% 0.95/1.63 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.95/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.95/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.63 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.95/1.63 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.95/1.63 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.63 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.95/1.63 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.63 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.95/1.63 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.95/1.63 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.95/1.63 .
% 0.95/1.63 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.95/1.63 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.63 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.95/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), ! hBOOL( hAPP( hAPP(
% 0.95/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 0.95/1.63 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.95/1.63 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X
% 0.95/1.63 ) ) }.
% 0.95/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.95/1.63 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.95/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.63 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.95/1.63 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.95/1.63 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.95/1.63 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.95/1.63 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.95/1.63 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol36( Z, Y
% 0.95/1.63 ), Y ) }.
% 0.95/1.63 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.95/1.63 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.63 skol36( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.95/1.63 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.95/1.63 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.95/1.63 , skol36( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.95/1.63 }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Int_Oint ) ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.95/1.63 = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Int_Oint ) ) ) }.
% 0.95/1.63 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Int_Oint ) ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.95/1.63 }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Int_Oint ) ), X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.63 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.63 tc_Int_Oint ) ), X ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.63 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.63 ), ! U = T }.
% 0.95/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.63 ), ! Z = Y }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.95/1.63 ) ), Z ) }.
% 0.95/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.63 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.63 ), U = Z, T = Y }.
% 0.95/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.63 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.63 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.63 ) }.
% 0.95/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.95/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.63 tc_Int_Oint ), X ) = X }.
% 0.95/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Int_Oint ) ) = X }.
% 0.95/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.63 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.95/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.95/1.63 ) ) }.
% 0.95/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.95/1.63 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.63 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.95/1.63 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.63 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.95/1.63 ) ), T ), Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.95/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.63 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.95/1.63 .
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.95/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.95/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.95/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.95/1.63 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.63 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.95/1.64 ( tc_Int_Oint ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.64 tc_Int_Oint ), X ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.64 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.95/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.64 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.95/1.64 ( tc_Int_Oint ) }.
% 0.95/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.64 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.95/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.64 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.95/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.95/1.64 tc_Int_Oint ) ) }.
% 0.95/1.64 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.64 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.64 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.95/1.64 .
% 0.95/1.64 { ! c_RealDef_Opositive( X ), ! c_RealDef_Opositive( Y ),
% 0.95/1.64 c_RealDef_Opositive( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.64 tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.95/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.95/1.64 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.95/1.64 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.95/1.64 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.64 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.64 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.64 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.64 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.64 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.64 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.95/1.64 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.64 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.95/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.95/1.64 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.64 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.95/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.95/1.64 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.64 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.64 ( X, Y ) ) }.
% 0.95/1.64 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.64 ) ), Y ) }.
% 0.95/1.64 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.64 ( X, Y ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.64 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.95/1.64 ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.64 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.95/1.64 ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.64 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 0.95/1.64 ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.64 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 0.95/1.64 ) ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.95/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.95/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.95/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.95/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.95/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.95/1.64 }.
% 0.95/1.64 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.95/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.95/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.95/1.64 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.95/1.64 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.95/1.64 ) }.
% 0.95/1.64 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.95/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.95/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.95/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.95/1.64 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.95/1.64 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.95/1.64 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.64 = Y }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.64 = Y }.
% 0.95/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.64 = Y }.
% 0.95/1.64 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.64 = Y }.
% 0.95/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.64 = Y }.
% 0.95/1.64 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.64 = Y }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.64 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.64 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.64 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.95/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.95/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.95/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.95/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.95/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.95/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.95/1.64 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.95/1.64 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.95/1.64 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.64 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.64 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.95/1.64 }.
% 0.95/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.64 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.64 ( X ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.64 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.64 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.64 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.64 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.64 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.64 ( X ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.64 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.64 ( X ) ), alpha8( X, Y, Z ), alpha18( X, Y, Z ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.64 ( X ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.64 ( X ) ) }.
% 0.95/1.64 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.64 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.64 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.95/1.64 ( X ), Y ), alpha18( X, Y, Z ) }.
% 0.95/1.64 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.64 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ), alpha8( X, Y, Z ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha9( X, Y
% 0.95/1.64 , Z ), alpha19( X, Y, Z ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.64 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.64 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ), alpha19( X, Y, Z ) }.
% 0.95/1.64 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.64 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), alpha9( X, Y, Z ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.64 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.64 ( X ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.64 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.95/1.64 .
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.95/1.64 .
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.64 ( X ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.64 ( X ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.64 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha10( X, Y, Z, T ),
% 0.95/1.64 alpha20( X, Y, Z, T ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z, T ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z, T ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.64 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.64 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha20( X, Y, Z, T ) }.
% 0.95/1.64 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.95/1.64 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.95/1.64 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha10( X, Y, Z, T ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha11( X, Y, Z, T ),
% 0.95/1.64 alpha21( X, Y, Z, T ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha11( X, Y, Z, T ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha21( X, Y, Z, T ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.64 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.64 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha21( X, Y, Z, T ) }.
% 0.95/1.64 { ! alpha11( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.64 { ! alpha11( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.64 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha11( X, Y, Z, T ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.64 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.95/1.64 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.95/1.64 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.64 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.64 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.95/1.64 ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.64 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.64 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.64 ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.64 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.64 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.95/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.95/1.64 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.95/1.64 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.64 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.95/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.95/1.64 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.64 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.95/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.95/1.64 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.95/1.64 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.64 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.95/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.64 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.64 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.64 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.95/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.64 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.95/1.64 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.95/1.64 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.95/1.64 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.64 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.95/1.64 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.64 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.64 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.95/1.64 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.95/1.64 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.64 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.95/1.64 ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.95/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.64 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.64 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.95/1.64 tc_Nat_Onat, Z, Y ) ) }.
% 0.95/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.95/1.64 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.95/1.64 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.64 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.64 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.64 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.64 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.64 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.64 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.64 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.64 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.64 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.95/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.95/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.64 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.64 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.64 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.64 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.64 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 0.95/1.64 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.64 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ) = hAPP(
% 0.95/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_NthRoot_Oroot
% 0.95/1.64 ( X, Z ) ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.95/1.64 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.64 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.95/1.64 c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.64 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.95/1.64 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.95/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.95/1.64 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.95/1.64 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.64 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.95/1.64 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.64 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.95/1.64 ), Y ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.95/1.64 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.64 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.64 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.95/1.64 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.95/1.64 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.64 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), c_NthRoot_Oroot( X
% 0.95/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Z )
% 0.95/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.95/1.64 c_NthRoot_Oroot( X, Y ) ), c_NthRoot_Oroot( X, Z ) ) }.
% 0.95/1.64 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.95/1.64 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.95/1.64 hAPP( Z, skol37( U, W, Z ) ) ) }.
% 0.95/1.64 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.95/1.64 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.95/1.64 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ),
% 0.95/1.64 c_Groups_Oplus__class_Oplus( X, skol37( X, Y, Z ),
% 0.95/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 0.95/1.64 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.95/1.64 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.64 , T, c_Groups_Ozero__class_Ozero( X ) ) ) ), ! hBOOL( hAPP( Z, T ) ),
% 0.95/1.64 hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.95/1.64 skol68( X, Y, Z ) ) ) ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.95/1.64 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.95/1.64 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.95/1.64 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.64 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.95/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.95/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.64 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.95/1.64 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.95/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.95/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.95/1.64 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) ), hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus
% 0.95/1.64 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ) ) }.
% 0.95/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.95/1.64 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.64 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.95/1.64 , Z ), X ) ), T ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.95/1.64 tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) )
% 0.95/1.64 }.
% 0.95/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 0.95/1.64 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.95/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 0.95/1.64 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.95/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.95/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.95/1.64 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.95/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.95/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.95/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.64 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 0.95/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.64 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.95/1.64 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.64 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.95/1.64 .
% 0.95/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.95/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.95/1.64 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.95/1.64 .
% 0.95/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.95/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.95/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.95/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.95/1.64 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.64 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.95/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.64 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.64 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.95/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.95/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.95/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.95/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.95/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.95/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.95/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 1.28/1.64 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.28/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ) }.
% 1.28/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ) }.
% 1.28/1.64 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.28/1.64 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.64 , Y ), X ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.28/1.64 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.28/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.28/1.64 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.28/1.64 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.28/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.28/1.64 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.28/1.64 ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.28/1.64 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.28/1.64 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.28/1.64 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.28/1.64 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.28/1.64 ), X ) ) }.
% 1.28/1.64 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.28/1.64 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.64 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.28/1.64 ( tc_Nat_Onat, X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.64 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.28/1.64 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.28/1.64 ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.28/1.64 ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), c_NthRoot_Oroot( hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z ) =
% 1.28/1.64 c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.28/1.64 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.28/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.28/1.64 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ) }.
% 1.28/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ), hBOOL( hAPP(
% 1.28/1.64 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.28/1.64 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 1.28/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ), hBOOL( hAPP( hAPP
% 1.28/1.64 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 1.28/1.64 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 Y ), X ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.28/1.64 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 X ), Y ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.28/1.64 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), c_NthRoot_Oroot(
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z ) =
% 1.28/1.64 c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 1.28/1.64 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Int_Oint ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, X, Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.28/1.64 ( tc_Int_Oint ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.64 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.28/1.64 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.28/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.64 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.28/1.64 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.64 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.64 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.28/1.64 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.28/1.64 , Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.28/1.64 ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.28/1.64 , Y ) ) ) }.
% 1.28/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.28/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.28/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.28/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.28/1.64 .
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Nat_Onat ), X ), Y ) }.
% 1.28/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.28/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.28/1.64 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.28/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol38( X, Y ) ), Y
% 1.28/1.64 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.28/1.64 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.28/1.64 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.28/1.64 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol39( Z, T ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol39( X, Y ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol40( Z, T ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol40( X, Y ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol41( Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol41( X ) ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.64 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.64 , alpha25( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha25( X, Y, Z, T ),
% 1.28/1.64 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.28/1.64 { ! alpha25( X, Y, Z, T ), alpha12( X, Z, T ) }.
% 1.28/1.64 { ! alpha25( X, Y, Z, T ), alpha22( X, Y, T ) }.
% 1.28/1.64 { ! alpha12( X, Z, T ), ! alpha22( X, Y, T ), alpha25( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha22( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), alpha26( X, Y, Z ) }.
% 1.28/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha22( X
% 1.28/1.64 , Y, Z ) }.
% 1.28/1.64 { ! alpha26( X, Y, Z ), alpha22( X, Y, Z ) }.
% 1.28/1.64 { ! alpha26( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha26( X
% 1.28/1.64 , Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.28/1.64 ), c_Polynomial_Odegree( X, Z ) ), alpha26( X, Y, Z ) }.
% 1.28/1.64 { ! alpha12( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha12( X,
% 1.28/1.64 Y, Z ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha12( X
% 1.28/1.64 , Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.28/1.64 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.28/1.64 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.64 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.64 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.64 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.28/1.64 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol42( Z, Y ) ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 1.28/1.64 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, skol42( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.64 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 1.28/1.64 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 1.28/1.64 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol43( Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol43( X ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol44( Z, T ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol44( X, Y ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol45( Z, T ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol45( X, Y ) ) ) }.
% 1.28/1.64 { c_Complex_Ocis( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Y ) ) ), X
% 1.28/1.64 ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.28/1.64 c_Complex_Ocis( X ) ), c_Complex_Ocis( hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ) ), X ) ) ) }.
% 1.28/1.64 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.28/1.64 c_Complex_Ocis( Y ) ), c_Complex_Ocis( X ) ) = c_Complex_Ocis(
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.28/1.64 { c_Complex_Ocis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { c_Complex_Ocis( X ) = c_Complex_Orcis( c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_RealDef_Oreal ), X ) }.
% 1.28/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.28/1.64 c_Complex_Ocis( Y ) ), X ) = c_Complex_Ocis( hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, X ) ), Y ) ) }.
% 1.28/1.64 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 1.28/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.28/1.64 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, skol46( X, Y ) ) ), X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, c_Nat_OSuc( skol46( X, Y ) ) ) ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, skol47( X, Y ) ) ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.64 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol48( X, Y ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.28/1.64 ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 tc_RealDef_Oreal, X, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.28/1.64 ), c_Transcendental_Oln( Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.28/1.64 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! X = Y,
% 1.28/1.64 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.28/1.64 ), X ) }.
% 1.28/1.64 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.28/1.64 ( X ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, X, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.28/1.64 ( X ), c_Transcendental_Oln( Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.28/1.64 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.28/1.64 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! X =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 1.28/1.64 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.28/1.64 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.28/1.64 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.28/1.64 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.28/1.64 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.28/1.64 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.28/1.64 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_RealDef_Oreal ), X ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_RealDef_Oreal, c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.28/1.64 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) ), X ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol49( X ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol50( X, Y ) ) ) }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.28/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.28/1.64 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.64 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.28/1.64 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.28/1.64 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.28/1.64 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.28/1.64 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.64 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.64 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.28/1.64 Z ) ), U ), T ) = Y }.
% 1.28/1.64 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.28/1.64 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), U ), Y ) }.
% 1.28/1.64 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.64 W ) ), U ), Y ) }.
% 1.28/1.64 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), U ), Y ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.64 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.28/1.64 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.64 Z ) ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.64 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.28/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.28/1.64 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 X, W, Z ) ), U ), T ), Y ) }.
% 1.28/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), U ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( X, Z, W ) ), U ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.64 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.28/1.64 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, U, T
% 1.28/1.64 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.28/1.64 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ), hBOOL( hAPP(
% 1.28/1.64 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.64 , U, T ) ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.28/1.64 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, U, T
% 1.28/1.64 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.28/1.64 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ), hBOOL( hAPP(
% 1.28/1.64 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.64 , U, T ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.64 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.28/1.64 ( X, Y ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.28/1.64 ) ) = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.28/1.64 , alpha13( X, Y, Z ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.28/1.64 , alpha23( X, Y, Z ) }.
% 1.28/1.64 { ! alpha13( X, Y, Z ), ! alpha23( X, Y, Z ), hBOOL( hAPP( Z,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.28/1.64 { ! alpha23( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.28/1.64 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, skol51( T, U, Z ) ) ), alpha23( X, Y, Z ) }.
% 1.28/1.64 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol51( X, Y, Z ) ),
% 1.28/1.64 alpha23( X, Y, Z ) }.
% 1.28/1.64 { ! alpha13( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.28/1.64 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha13( X, Y, Z ) }
% 1.28/1.64 .
% 1.28/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13
% 1.28/1.64 ( X, Y, Z ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.28/1.64 , ! alpha14( X, Y, Z ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.28/1.64 , ! alpha24( X, Y, Z ) }.
% 1.28/1.64 { alpha14( X, Y, Z ), alpha24( X, Y, Z ), hBOOL( hAPP( Z,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.28/1.64 { ! alpha24( X, Y, Z ), ! hBOOL( hAPP( Z, skol52( T, U, Z ) ) ) }.
% 1.28/1.64 { ! alpha24( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.28/1.64 skol52( X, Y, Z ) ) }.
% 1.28/1.64 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.28/1.64 ) ), alpha24( X, Y, Z ) }.
% 1.28/1.64 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.28/1.64 }.
% 1.28/1.64 { ! alpha14( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha14( X, Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.28/1.64 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.64 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.28/1.64 ( tc_fun( Y, X ) ) }.
% 1.28/1.64 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.28/1.64 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.28/1.64 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.64 tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.28/1.64 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.28/1.64 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.28/1.64 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.28/1.64 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.28/1.64 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.28/1.64 { class_Power_Opower( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.28/1.64 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.28/1.64 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.28/1.64 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.64 tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.28/1.64 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.28/1.64 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.28/1.64 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.28/1.64 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.28/1.64 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.28/1.64 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.64 tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.28/1.64 .
% 1.28/1.64 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 1.28/1.64 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.64 tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ),
% 1.28/1.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.64 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.64 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.28/1.64 X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.64 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.64 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.64 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.64 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.64 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.64 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.28/1.64 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.64 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.64 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.64 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.64 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.64 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.28/1.64 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.28/1.64 ( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.28/1.64 ( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.28/1.64 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.28/1.64 { alpha32( X, skol53( X ) ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 tc_RealDef_Oreal, skol53( X ), X ), v_thesis____ }.
% 1.28/1.64 { alpha32( X, skol53( X ) ), ! alpha15( Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol53( X ), Y ),
% 1.28/1.64 v_thesis____ }.
% 1.28/1.64 { ! alpha32( X, Y ), alpha29( Y ) }.
% 1.28/1.64 { ! alpha32( X, Y ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 1.28/1.64 X ) }.
% 1.28/1.64 { ! alpha29( Y ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.28/1.64 alpha32( X, Y ) }.
% 1.28/1.64 { ! alpha29( X ), alpha15( skol54( Y ) ) }.
% 1.28/1.64 { ! alpha29( X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.28/1.64 skol54( X ) ) }.
% 1.28/1.64 { ! alpha15( Y ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y )
% 1.28/1.64 , alpha29( X ) }.
% 1.28/1.64 { ! alpha15( X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, skol55( Y ) ), v_r
% 1.28/1.64 ) }.
% 1.28/1.64 { ! alpha15( X ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.28/1.64 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol55( X ) ) ) =
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ), v_r ), !
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.28/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), Y ) ) =
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), alpha15( X ) }.
% 1.28/1.64 { ! v_thesis____ }.
% 1.28/1.64
% 1.28/1.64 *** allocated 15000 integers for clauses
% 1.28/1.64 *** allocated 22500 integers for clauses
% 1.28/1.64 *** allocated 33750 integers for clauses
% 1.28/1.64 *** allocated 50625 integers for clauses
% 1.28/1.64 *** allocated 75937 integers for clauses
% 1.28/1.64 percentage equality = 0.242473, percentage horn = 0.915058
% 1.28/1.64 This is a problem with some equality
% 1.28/1.64
% 1.28/1.64
% 1.28/1.64
% 1.28/1.64 Options Used:
% 1.28/1.64
% 1.28/1.64 useres = 1
% 1.28/1.64 useparamod = 1
% 1.28/1.64 useeqrefl = 1
% 1.28/1.64 useeqfact = 1
% 1.28/1.64 usefactor = 1
% 1.28/1.64 usesimpsplitting = 0
% 1.28/1.64 usesimpdemod = 5
% 1.28/1.64 usesimpres = 3
% 1.28/1.64
% 1.28/1.64 resimpinuse = 1000
% 1.28/1.64 resimpclauses = 20000
% 1.28/1.64 substype = eqrewr
% 1.28/1.64 backwardsubs = 1
% 1.28/1.64 selectoldest = 5
% 1.28/1.64
% 1.28/1.64 litorderings [0] = split
% 1.28/1.64 litorderings [1] = extend the termordering, first sorting on arguments
% 1.28/1.64
% 1.28/1.64 termordering = kbo
% 1.28/1.64
% 1.28/1.64 litapriori = 0
% 1.28/1.64 termapriori = 1
% 1.28/1.64 litaposteriori = 0
% 1.28/1.64 termaposteriori = 0
% 1.28/1.64 demodaposteriori = 0
% 1.28/1.64 ordereqreflfact = 0
% 1.28/1.64
% 1.28/1.64 litselect = negord
% 1.28/1.64
% 1.28/1.64 maxweight = 15
% 1.28/1.64 maxdepth = 30000
% 1.28/1.64 maxlength = 115
% 1.28/1.64 maxnrvars = 195
% 1.28/1.64 excuselevel = 1
% 1.28/1.64 increasemaxweight = 1
% 1.28/1.64
% 1.28/1.64 maxselected = 10000000
% 1.28/1.64 maxnrclauses = 10000000
% 1.28/1.64
% 1.28/1.64 showgenerated = 0
% 1.28/1.64 showkept = 0
% 1.28/1.64 showselected = 0
% 1.28/1.64 showdeleted = 0
% 1.28/1.64 showresimp = 1
% 1.28/1.64 showstatus = 2000
% 1.28/1.64
% 1.28/1.64 prologoutput = 0
% 1.28/1.64 nrgoals = 5000000
% 1.28/1.64 totalproof = 1
% 1.28/1.64
% 1.28/1.64 Symbols occurring in the translation:
% 1.28/1.64
% 1.28/1.64 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.28/1.64 . [1, 2] (w:1, o:215, a:1, s:1, b:0),
% 1.28/1.64 ! [4, 1] (w:0, o:119, a:1, s:1, b:0),
% 1.28/1.64 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.28/1.64 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.28/1.64 hAPP [38, 2] (w:1, o:239, a:1, s:1, b:0),
% 1.28/1.64 tc_RealDef_Oreal [39, 0] (w:1, o:19, a:1, s:1, b:0),
% 1.28/1.64 c_Groups_Ozero__class_Ozero [40, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.28/1.64 v_r [41, 0] (w:1, o:20, a:1, s:1, b:0),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq [42, 3] (w:1, o:305, a:1, s:1, b:0)
% 1.28/1.64 ,
% 1.28/1.64 tc_Complex_Ocomplex [46, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm [47, 2] (w:1, o:240, a:1, s:1, b:0),
% 1.28/1.64
% 1.28/1.64 v_p [48, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.28/1.64 c_Polynomial_Opoly [49, 2] (w:1, o:241, a:1, s:1, b:0),
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus [50, 2] (w:1, o:243, a:1, s:1, b:0),
% 1.28/1.64
% 1.28/1.64 c_Orderings_Oord__class_Oless [51, 3] (w:1, o:306, a:1, s:1, b:0),
% 1.28/1.64 c_Groups_Oone__class_Oone [55, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.28/1.64 class_Orderings_Opreorder [58, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.28/1.64 class_Rings_Ocomm__ring [60, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.28/1.64 tc_Polynomial_Opoly [61, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.28/1.64 class_RealVector_Oreal__normed__vector [62, 1] (w:1, o:141, a:1, s:1
% 1.28/1.64 , b:0),
% 1.28/1.64 class_Groups_Oordered__ab__group__add [67, 1] (w:1, o:143, a:1, s:1
% 1.28/1.64 , b:0),
% 1.28/1.64 class_RealVector_Oreal__normed__algebra__1 [68, 1] (w:1, o:144, a:1
% 1.28/1.64 , s:1, b:0),
% 1.28/1.64 class_Rings_Ocomm__semiring__1 [69, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.28/1.64 class_Rings_Ocomm__semiring__0 [70, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.28/1.64 class_Groups_Oone [71, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.28/1.64 class_Groups_Ozero [72, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.28/1.64 class_Groups_Olinordered__ab__group__add [73, 1] (w:1, o:150, a:1, s:
% 1.28/1.64 1, b:0),
% 1.28/1.64 class_Groups_Ogroup__add [74, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.28/1.64 class_Orderings_Olinorder [76, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.28/1.64 class_Orderings_Oord [78, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.28/1.64 tc_fun [79, 2] (w:1, o:283, a:1, s:1, b:0),
% 1.28/1.64 class_Orderings_Oorder [81, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.28/1.64 class_Int_Oring__char__0 [91, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.28/1.64 class_Rings_Oidom [92, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.28/1.64 class_Rings_Olinordered__idom [93, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.28/1.64 class_Rings_Olinordered__semidom [94, 1] (w:1, o:158, a:1, s:1, b:0)
% 1.28/1.64 ,
% 1.28/1.64 class_Lattices_Oboolean__algebra [95, 1] (w:1, o:160, a:1, s:1, b:0)
% 1.28/1.64 ,
% 1.28/1.64 class_Rings_Ozero__neq__one [98, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.28/1.64 c_Groups_Osgn__class_Osgn [99, 2] (w:1, o:284, a:1, s:1, b:0),
% 1.28/1.64 class_Groups_Osgn__if [100, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.28/1.64 class_Groups_Oab__group__add [101, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.28/1.64 class_Groups_Ouminus [103, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.28/1.64 c_Polynomial_Oorder [104, 3] (w:1, o:307, a:1, s:1, b:0),
% 1.28/1.64 tc_Nat_Onat [105, 0] (w:1, o:66, a:1, s:1, b:0),
% 1.28/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [106, 2] (w:1, o:
% 1.28/1.64 242, a:1, s:1, b:0),
% 1.28/1.64 c_Polynomial_Opoly__rec [107, 5] (w:1, o:361, a:1, s:1, b:0),
% 1.28/1.64 c_Polynomial_Opos__poly [108, 2] (w:1, o:285, a:1, s:1, b:0),
% 1.28/1.64 c_RealDef_Opositive [109, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.28/1.65 c_SEQ_OBseq [111, 2] (w:1, o:287, a:1, s:1, b:0),
% 1.28/1.65 c_Complex_Orcis [114, 2] (w:1, o:288, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Ocoeff [116, 2] (w:1, o:289, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_OpCons [117, 3] (w:1, o:308, a:1, s:1, b:0),
% 1.28/1.65 c_fequal [118, 2] (w:1, o:290, a:1, s:1, b:0),
% 1.28/1.65 c_If [119, 4] (w:1, o:347, a:1, s:1, b:0),
% 1.28/1.65 c_Rings_Odvd__class_Odvd [122, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.28/1.65 hBOOL [123, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.28/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [125, 3] (w:
% 1.28/1.65 1, o:309, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Osynthetic__div [126, 3] (w:1, o:310, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Ocomm__ring__1 [133, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.28/1.65 c_SEQ_Odecseq [135, 2] (w:1, o:291, a:1, s:1, b:0),
% 1.28/1.65 c_Power_Opower__class_Opower [136, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.28/1.65 c_SEQ_Oincseq [137, 2] (w:1, o:292, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Odegree [139, 2] (w:1, o:293, a:1, s:1, b:0),
% 1.28/1.65 c_Nat_Onat_Onat__case [140, 3] (w:1, o:304, a:1, s:1, b:0),
% 1.28/1.65 class_RealVector_Oreal__normed__div__algebra [141, 1] (w:1, o:169, a:
% 1.28/1.65 1, s:1, b:0),
% 1.28/1.65 class_Groups_Omonoid__mult [146, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Oring__1__no__zero__divisors [147, 1] (w:1, o:171, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 class_Power_Opower [148, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Omult__zero [149, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Ono__zero__divisors [150, 1] (w:1, o:179, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 class_Rings_Osemiring__0 [151, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.28/1.65 c_Nat_OSuc [152, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.28/1.65 tc_Int_Oint [158, 0] (w:1, o:99, a:1, s:1, b:0),
% 1.28/1.65 class_Fields_Ofield [160, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Opoly__gcd [161, 3] (w:1, o:311, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_OAbs__poly [162, 2] (w:1, o:294, a:1, s:1, b:0),
% 1.28/1.65 c_Orderings_Oorder_Omono [166, 4] (w:1, o:348, a:1, s:1, b:0),
% 1.28/1.65 c_RealDef_Oreal [168, 2] (w:1, o:286, a:1, s:1, b:0),
% 1.28/1.65 c_RComplete_Onatfloor [170, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.28/1.65 c_RComplete_Onatceiling [171, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.28/1.65 c_Groups_Oplus__class_Oplus [172, 3] (w:1, o:312, a:1, s:1, b:0),
% 1.28/1.65 c_NthRoot_Oroot [173, 2] (w:1, o:295, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Ocomm__monoid__add [175, 1] (w:1, o:187, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 class_Groups_Oab__semigroup__add [176, 1] (w:1, o:188, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 class_Groups_Ocancel__semigroup__add [177, 1] (w:1, o:189, a:1, s:1
% 1.28/1.65 , b:0),
% 1.28/1.65 class_Groups_Ocancel__ab__semigroup__add [178, 1] (w:1, o:190, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le [179, 1] (w:1, o:
% 1.28/1.65 191, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Oordered__cancel__ab__semigroup__add [180, 1] (w:1, o:
% 1.28/1.65 192, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Oordered__ab__semigroup__add [181, 1] (w:1, o:193, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.28/1.65 182, 1] (w:1, o:202, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Omonoid__add [183, 1] (w:1, o:203, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Oordered__comm__monoid__add [184, 1] (w:1, o:204, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 c_Groups_Otimes__class_Otimes [188, 1] (w:1, o:205, a:1, s:1, b:0),
% 1.28/1.65 class_RealVector_Oreal__normed__algebra [192, 1] (w:1, o:194, a:1, s:
% 1.28/1.65 1, b:0),
% 1.28/1.65 class_Rings_Ocomm__semiring [198, 1] (w:1, o:195, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Osemiring [200, 1] (w:1, o:196, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Oring [203, 1] (w:1, o:180, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Odvd [204, 1] (w:1, o:197, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Ocomm__monoid__mult [205, 1] (w:1, o:206, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 class_Groups_Oab__semigroup__mult [210, 1] (w:1, o:207, a:1, s:1, b:0
% 1.28/1.65 ),
% 1.28/1.65 class_Lattices_Oab__semigroup__idem__mult [212, 1] (w:1, o:159, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 class_Rings_Oring__no__zero__divisors [213, 1] (w:1, o:181, a:1, s:1
% 1.28/1.65 , b:0),
% 1.28/1.65 class_Rings_Oordered__cancel__semiring [214, 1] (w:1, o:198, a:1, s:1
% 1.28/1.65 , b:0),
% 1.48/1.88 class_Rings_Oordered__ring [215, 1] (w:1, o:199, a:1, s:1, b:0),
% 1.48/1.88 class_Rings_Oordered__semiring [216, 1] (w:1, o:200, a:1, s:1, b:0),
% 1.48/1.88
% 1.48/1.88 class_Rings_Oordered__comm__semiring [217, 1] (w:1, o:201, a:1, s:1
% 1.48/1.88 , b:0),
% 1.48/1.88 class_Rings_Olinordered__ring__strict [218, 1] (w:1, o:156, a:1, s:1
% 1.48/1.88 , b:0),
% 1.48/1.88 class_Rings_Olinordered__ring [219, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.48/1.88 class_Rings_Olinordered__comm__semiring__strict [220, 1] (w:1, o:173
% 1.48/1.88 , a:1, s:1, b:0),
% 1.48/1.88 class_Rings_Olinordered__semiring__strict [221, 1] (w:1, o:174, a:1
% 1.48/1.88 , s:1, b:0),
% 1.48/1.88 class_Rings_Olinordered__semiring [223, 1] (w:1, o:175, a:1, s:1, b:0
% 1.48/1.88 ),
% 1.48/1.88 class_Rings_Oring__1 [224, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.48/1.88 class_Rings_Olinordered__semiring__1 [226, 1] (w:1, o:176, a:1, s:1
% 1.48/1.88 , b:0),
% 1.48/1.88 class_Rings_Olinordered__semiring__1__strict [227, 1] (w:1, o:177, a:
% 1.48/1.88 1, s:1, b:0),
% 1.48/1.88 c_Polynomial_Opcompose [228, 3] (w:1, o:313, a:1, s:1, b:0),
% 1.48/1.88 c_Power_Opower_Opower [234, 3] (w:1, o:314, a:1, s:1, b:0),
% 1.48/1.88 c_Polynomial_Opdivmod__rel [240, 5] (w:1, o:362, a:1, s:1, b:0),
% 1.48/1.88 c_Complex_Ocis [243, 1] (w:1, o:208, a:1, s:1, b:0),
% 1.48/1.88 c_Complex_Oexpi [244, 1] (w:1, o:209, a:1, s:1, b:0),
% 1.48/1.88 c_Transcendental_Oln [245, 1] (w:1, o:210, a:1, s:1, b:0),
% 1.48/1.88 c_Groups_Ominus__class_Ominus [246, 3] (w:1, o:315, a:1, s:1, b:0),
% 1.48/1.88 class_Groups_Ocancel__comm__monoid__add [251, 1] (w:1, o:211, a:1, s:
% 1.48/1.88 1, b:0),
% 1.48/1.88 tc_HOL_Obool [253, 0] (w:1, o:98, a:1, s:1, b:0),
% 1.48/1.88 v_thesis____ [254, 0] (w:1, o:118, a:1, s:1, b:0),
% 1.48/1.88 alpha1 [255, 1] (w:1, o:212, a:1, s:1, b:1),
% 1.48/1.88 alpha2 [256, 3] (w:1, o:321, a:1, s:1, b:1),
% 1.48/1.88 alpha3 [257, 2] (w:1, o:296, a:1, s:1, b:1),
% 1.48/1.88 alpha4 [258, 2] (w:1, o:298, a:1, s:1, b:1),
% 1.48/1.88 alpha5 [259, 2] (w:1, o:299, a:1, s:1, b:1),
% 1.48/1.88 alpha6 [260, 2] (w:1, o:300, a:1, s:1, b:1),
% 1.48/1.88 alpha7 [261, 2] (w:1, o:301, a:1, s:1, b:1),
% 1.48/1.88 alpha8 [262, 3] (w:1, o:322, a:1, s:1, b:1),
% 1.48/1.88 alpha9 [263, 3] (w:1, o:323, a:1, s:1, b:1),
% 1.48/1.88 alpha10 [264, 4] (w:1, o:349, a:1, s:1, b:1),
% 1.48/1.88 alpha11 [265, 4] (w:1, o:350, a:1, s:1, b:1),
% 1.48/1.88 alpha12 [266, 3] (w:1, o:316, a:1, s:1, b:1),
% 1.48/1.88 alpha13 [267, 3] (w:1, o:317, a:1, s:1, b:1),
% 1.48/1.88 alpha14 [268, 3] (w:1, o:318, a:1, s:1, b:1),
% 1.48/1.88 alpha15 [269, 1] (w:1, o:213, a:1, s:1, b:1),
% 1.48/1.88 alpha16 [270, 2] (w:1, o:302, a:1, s:1, b:1),
% 1.48/1.88 alpha17 [271, 2] (w:1, o:303, a:1, s:1, b:1),
% 1.48/1.88 alpha18 [272, 3] (w:1, o:319, a:1, s:1, b:1),
% 1.48/1.88 alpha19 [273, 3] (w:1, o:320, a:1, s:1, b:1),
% 1.48/1.88 alpha20 [274, 4] (w:1, o:351, a:1, s:1, b:1),
% 1.48/1.88 alpha21 [275, 4] (w:1, o:352, a:1, s:1, b:1),
% 1.48/1.88 alpha22 [276, 3] (w:1, o:324, a:1, s:1, b:1),
% 1.48/1.88 alpha23 [277, 3] (w:1, o:325, a:1, s:1, b:1),
% 1.48/1.88 alpha24 [278, 3] (w:1, o:326, a:1, s:1, b:1),
% 1.48/1.88 alpha25 [279, 4] (w:1, o:353, a:1, s:1, b:1),
% 1.48/1.88 alpha26 [280, 3] (w:1, o:327, a:1, s:1, b:1),
% 1.48/1.88 alpha27 [281, 3] (w:1, o:328, a:1, s:1, b:1),
% 1.48/1.88 alpha28 [282, 3] (w:1, o:329, a:1, s:1, b:1),
% 1.48/1.88 alpha29 [283, 1] (w:1, o:214, a:1, s:1, b:1),
% 1.48/1.88 alpha30 [284, 3] (w:1, o:330, a:1, s:1, b:1),
% 1.48/1.88 alpha31 [285, 4] (w:1, o:354, a:1, s:1, b:1),
% 1.48/1.88 alpha32 [286, 2] (w:1, o:297, a:1, s:1, b:1),
% 1.48/1.88 alpha33 [287, 4] (w:1, o:355, a:1, s:1, b:1),
% 1.48/1.88 alpha34 [288, 4] (w:1, o:356, a:1, s:1, b:1),
% 1.48/1.88 skol1 [289, 2] (w:1, o:244, a:1, s:1, b:1),
% 1.48/1.88 skol2 [290, 0] (w:1, o:14, a:1, s:1, b:1),
% 1.48/1.88 skol3 [291, 1] (w:1, o:131, a:1, s:1, b:1),
% 1.48/1.88 skol4 [292, 0] (w:1, o:15, a:1, s:1, b:1),
% 1.48/1.88 skol5 [293, 0] (w:1, o:16, a:1, s:1, b:1),
% 1.48/1.88 skol6 [294, 0] (w:1, o:18, a:1, s:1, b:1),
% 1.48/1.88 skol7 [295, 3] (w:1, o:335, a:1, s:1, b:1),
% 1.48/1.88 skol8 [296, 2] (w:1, o:247, a:1, s:1, b:1),
% 1.48/1.88 skol9 [297, 2] (w:1, o:248, a:1, s:1, b:1),
% 1.48/1.88 skol10 [298, 3] (w:1, o:336, a:1, s:1, b:1),
% 1.48/1.88 skol11 [299, 3] (w:1, o:337, a:1, s:1, b:1),
% 1.48/1.88 skol12 [300, 2] (w:1, o:249, a:1, s:1, b:1),
% 1.48/1.88 skol13 [301, 2] (w:1, o:250, a:1, s:1, b:1),
% 1.48/1.88 skol14 [302, 2] (w:1, o:251, a:1, s:1, b:1),
% 1.48/1.88 skol15 [303, 4] (w:1, o:357, a:1, s:1, b:1),
% 6.70/7.13 skol16 [304, 2] (w:1, o:252, a:1, s:1, b:1),
% 6.70/7.13 skol17 [305, 1] (w:1, o:132, a:1, s:1, b:1),
% 6.70/7.13 skol18 [306, 3] (w:1, o:338, a:1, s:1, b:1),
% 6.70/7.13 skol19 [307, 4] (w:1, o:358, a:1, s:1, b:1),
% 6.70/7.13 skol20 [308, 3] (w:1, o:339, a:1, s:1, b:1),
% 6.70/7.13 skol21 [309, 3] (w:1, o:340, a:1, s:1, b:1),
% 6.70/7.13 skol22 [310, 3] (w:1, o:341, a:1, s:1, b:1),
% 6.70/7.13 skol23 [311, 2] (w:1, o:253, a:1, s:1, b:1),
% 6.70/7.13 skol24 [312, 2] (w:1, o:254, a:1, s:1, b:1),
% 6.70/7.13 skol25 [313, 2] (w:1, o:255, a:1, s:1, b:1),
% 6.70/7.13 skol26 [314, 2] (w:1, o:256, a:1, s:1, b:1),
% 6.70/7.13 skol27 [315, 1] (w:1, o:130, a:1, s:1, b:1),
% 6.70/7.13 skol28 [316, 2] (w:1, o:257, a:1, s:1, b:1),
% 6.70/7.13 skol29 [317, 2] (w:1, o:258, a:1, s:1, b:1),
% 6.70/7.13 skol30 [318, 2] (w:1, o:259, a:1, s:1, b:1),
% 6.70/7.13 skol31 [319, 2] (w:1, o:260, a:1, s:1, b:1),
% 6.70/7.13 skol32 [320, 2] (w:1, o:261, a:1, s:1, b:1),
% 6.70/7.13 skol33 [321, 2] (w:1, o:262, a:1, s:1, b:1),
% 6.70/7.13 skol34 [322, 2] (w:1, o:263, a:1, s:1, b:1),
% 6.70/7.13 skol35 [323, 2] (w:1, o:264, a:1, s:1, b:1),
% 6.70/7.13 skol36 [324, 2] (w:1, o:265, a:1, s:1, b:1),
% 6.70/7.13 skol37 [325, 3] (w:1, o:342, a:1, s:1, b:1),
% 6.70/7.13 skol38 [326, 2] (w:1, o:266, a:1, s:1, b:1),
% 6.70/7.13 skol39 [327, 2] (w:1, o:267, a:1, s:1, b:1),
% 6.70/7.13 skol40 [328, 2] (w:1, o:268, a:1, s:1, b:1),
% 6.70/7.13 skol41 [329, 1] (w:1, o:133, a:1, s:1, b:1),
% 6.70/7.13 skol42 [330, 2] (w:1, o:269, a:1, s:1, b:1),
% 6.70/7.13 skol43 [331, 1] (w:1, o:134, a:1, s:1, b:1),
% 6.70/7.13 skol44 [332, 2] (w:1, o:270, a:1, s:1, b:1),
% 6.70/7.13 skol45 [333, 2] (w:1, o:271, a:1, s:1, b:1),
% 6.70/7.13 skol46 [334, 2] (w:1, o:272, a:1, s:1, b:1),
% 6.70/7.13 skol47 [335, 2] (w:1, o:273, a:1, s:1, b:1),
% 6.70/7.13 skol48 [336, 2] (w:1, o:274, a:1, s:1, b:1),
% 6.70/7.13 skol49 [337, 1] (w:1, o:135, a:1, s:1, b:1),
% 6.70/7.13 skol50 [338, 2] (w:1, o:275, a:1, s:1, b:1),
% 6.70/7.13 skol51 [339, 3] (w:1, o:343, a:1, s:1, b:1),
% 6.70/7.13 skol52 [340, 3] (w:1, o:344, a:1, s:1, b:1),
% 6.70/7.13 skol53 [341, 1] (w:1, o:136, a:1, s:1, b:1),
% 6.70/7.13 skol54 [342, 1] (w:1, o:137, a:1, s:1, b:1),
% 6.70/7.13 skol55 [343, 1] (w:1, o:138, a:1, s:1, b:1),
% 6.70/7.13 skol56 [344, 1] (w:1, o:139, a:1, s:1, b:1),
% 6.70/7.13 skol57 [345, 0] (w:1, o:17, a:1, s:1, b:1),
% 6.70/7.13 skol58 [346, 3] (w:1, o:345, a:1, s:1, b:1),
% 6.70/7.13 skol59 [347, 2] (w:1, o:276, a:1, s:1, b:1),
% 6.70/7.13 skol60 [348, 2] (w:1, o:277, a:1, s:1, b:1),
% 6.70/7.13 skol61 [349, 2] (w:1, o:278, a:1, s:1, b:1),
% 6.70/7.13 skol62 [350, 2] (w:1, o:279, a:1, s:1, b:1),
% 6.70/7.13 skol63 [351, 3] (w:1, o:331, a:1, s:1, b:1),
% 6.70/7.13 skol64 [352, 3] (w:1, o:332, a:1, s:1, b:1),
% 6.70/7.13 skol65 [353, 2] (w:1, o:280, a:1, s:1, b:1),
% 6.70/7.13 skol66 [354, 2] (w:1, o:281, a:1, s:1, b:1),
% 6.70/7.13 skol67 [355, 2] (w:1, o:282, a:1, s:1, b:1),
% 6.70/7.13 skol68 [356, 3] (w:1, o:333, a:1, s:1, b:1),
% 6.70/7.13 skol69 [357, 3] (w:1, o:334, a:1, s:1, b:1),
% 6.70/7.13 skol70 [358, 3] (w:1, o:346, a:1, s:1, b:1),
% 6.70/7.13 skol71 [359, 4] (w:1, o:359, a:1, s:1, b:1),
% 6.70/7.13 skol72 [360, 4] (w:1, o:360, a:1, s:1, b:1),
% 6.70/7.13 skol73 [361, 2] (w:1, o:245, a:1, s:1, b:1),
% 6.70/7.13 skol74 [362, 2] (w:1, o:246, a:1, s:1, b:1).
% 6.70/7.13
% 6.70/7.13
% 6.70/7.13 Starting Search:
% 6.70/7.13
% 6.70/7.13 *** allocated 113905 integers for clauses
% 6.70/7.13 *** allocated 170857 integers for clauses
% 6.70/7.13 Resimplifying inuse:
% 6.70/7.13 Done
% 6.70/7.13
% 6.70/7.13
% 6.70/7.13 Intermediate Status:
% 6.70/7.13 Generated: 2960
% 6.70/7.13 Kept: 2004
% 6.70/7.13 Inuse: 51
% 6.70/7.13 Deleted: 0
% 6.70/7.13 Deletedinuse: 0
% 6.70/7.13
% 6.70/7.13 *** allocated 256285 integers for clauses
% 6.70/7.13 Resimplifying inuse:
% 6.70/7.13 Done
% 6.70/7.13
% 6.70/7.13 *** allocated 170857 integers for termspace/termends
% 6.70/7.13 *** allocated 384427 integers for clauses
% 6.70/7.13
% 6.70/7.13 Intermediate Status:
% 6.70/7.13 Generated: 6135
% 6.70/7.13 Kept: 4195
% 6.70/7.13 Inuse: 176
% 6.70/7.13 Deleted: 2
% 6.70/7.13 Deletedinuse: 2
% 6.70/7.13
% 6.70/7.13 Resimplifying inuse:
% 6.70/7.13 Done
% 6.70/7.13
% 6.70/7.13 Resimplifying inuse:
% 6.70/7.13 Done
% 6.70/7.13
% 6.70/7.13
% 6.70/7.13 Intermediate Status:
% 6.70/7.13 Generated: 8990
% 6.70/7.13 Kept: 6212
% 6.70/7.13 Inuse: 268
% 6.70/7.13 Deleted: 4
% 6.70/7.13 Deletedinuse: 2
% 6.70/7.13
% 6.70/7.13 Resimplifying inuse:
% 6.70/7.13 Done
% 6.70/7.13
% 6.70/7.13 *** allocated 256285 integers for termspace/termends
% 6.70/7.13 *** allocated 576640 integers for clauses
% 6.70/7.13 Resimplifying inuse:
% 6.70/7.13 Done
% 6.70/7.13
% 6.70/7.13
% 6.70/7.13 Intermediate Status:
% 6.70/7.13 Generated: 13011
% 6.70/7.13 Kept: 8224
% 6.70/7.13 Inuse: 333
% 6.70/7.13 Deleted: 4
% 6.70/7.13 Deletedinuse: 2
% 6.70/7.13
% 6.70/7.13 Resimplifying inuse:
% 6.70/7.13 Done
% 6.70/7.13
% 6.70/7.13 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 17352
% 32.68/33.07 Kept: 10228
% 32.68/33.07 Inuse: 390
% 32.68/33.07 Deleted: 5
% 32.68/33.07 Deletedinuse: 2
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 *** allocated 864960 integers for clauses
% 32.68/33.07 *** allocated 384427 integers for termspace/termends
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 22874
% 32.68/33.07 Kept: 12608
% 32.68/33.07 Inuse: 432
% 32.68/33.07 Deleted: 6
% 32.68/33.07 Deletedinuse: 2
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 28956
% 32.68/33.07 Kept: 14670
% 32.68/33.07 Inuse: 457
% 32.68/33.07 Deleted: 9
% 32.68/33.07 Deletedinuse: 5
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 33170
% 32.68/33.07 Kept: 17221
% 32.68/33.07 Inuse: 487
% 32.68/33.07 Deleted: 9
% 32.68/33.07 Deletedinuse: 5
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 *** allocated 1297440 integers for clauses
% 32.68/33.07 *** allocated 576640 integers for termspace/termends
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 36207
% 32.68/33.07 Kept: 19239
% 32.68/33.07 Inuse: 502
% 32.68/33.07 Deleted: 9
% 32.68/33.07 Deletedinuse: 5
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying clauses:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 40264
% 32.68/33.07 Kept: 21244
% 32.68/33.07 Inuse: 543
% 32.68/33.07 Deleted: 546
% 32.68/33.07 Deletedinuse: 5
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 44089
% 32.68/33.07 Kept: 23289
% 32.68/33.07 Inuse: 581
% 32.68/33.07 Deleted: 546
% 32.68/33.07 Deletedinuse: 5
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 49207
% 32.68/33.07 Kept: 26330
% 32.68/33.07 Inuse: 622
% 32.68/33.07 Deleted: 546
% 32.68/33.07 Deletedinuse: 5
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 54686
% 32.68/33.07 Kept: 28378
% 32.68/33.07 Inuse: 642
% 32.68/33.07 Deleted: 546
% 32.68/33.07 Deletedinuse: 5
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 *** allocated 1946160 integers for clauses
% 32.68/33.07 *** allocated 864960 integers for termspace/termends
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 60783
% 32.68/33.07 Kept: 30423
% 32.68/33.07 Inuse: 662
% 32.68/33.07 Deleted: 546
% 32.68/33.07 Deletedinuse: 5
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 63849
% 32.68/33.07 Kept: 32425
% 32.68/33.07 Inuse: 678
% 32.68/33.07 Deleted: 546
% 32.68/33.07 Deletedinuse: 5
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 66972
% 32.68/33.07 Kept: 34432
% 32.68/33.07 Inuse: 694
% 32.68/33.07 Deleted: 546
% 32.68/33.07 Deletedinuse: 5
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 71093
% 32.68/33.07 Kept: 36442
% 32.68/33.07 Inuse: 734
% 32.68/33.07 Deleted: 546
% 32.68/33.07 Deletedinuse: 5
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 78225
% 32.68/33.07 Kept: 39123
% 32.68/33.07 Inuse: 757
% 32.68/33.07 Deleted: 547
% 32.68/33.07 Deletedinuse: 6
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 84219
% 32.68/33.07 Kept: 41259
% 32.68/33.07 Inuse: 772
% 32.68/33.07 Deleted: 547
% 32.68/33.07 Deletedinuse: 6
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying clauses:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 90587
% 32.68/33.07 Kept: 43266
% 32.68/33.07 Inuse: 792
% 32.68/33.07 Deleted: 1291
% 32.68/33.07 Deletedinuse: 6
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 *** allocated 1297440 integers for termspace/termends
% 32.68/33.07 *** allocated 2919240 integers for clauses
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 97904
% 32.68/33.07 Kept: 46774
% 32.68/33.07 Inuse: 812
% 32.68/33.07 Deleted: 1291
% 32.68/33.07 Deletedinuse: 6
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 103619
% 32.68/33.07 Kept: 48791
% 32.68/33.07 Inuse: 831
% 32.68/33.07 Deleted: 1291
% 32.68/33.07 Deletedinuse: 6
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 106716
% 32.68/33.07 Kept: 50876
% 32.68/33.07 Inuse: 837
% 32.68/33.07 Deleted: 1291
% 32.68/33.07 Deletedinuse: 6
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 114346
% 32.68/33.07 Kept: 53584
% 32.68/33.07 Inuse: 862
% 32.68/33.07 Deleted: 1291
% 32.68/33.07 Deletedinuse: 6
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 122608
% 32.68/33.07 Kept: 56163
% 32.68/33.07 Inuse: 877
% 32.68/33.07 Deleted: 1291
% 32.68/33.07 Deletedinuse: 6
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07 Resimplifying inuse:
% 32.68/33.07 Done
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 129844
% 32.68/33.07 Kept: 58238
% 32.68/33.07 Inuse: 886
% 32.68/33.07 Deleted: 1291
% 32.68/33.07 Deletedinuse: 6
% 32.68/33.07
% 32.68/33.07
% 32.68/33.07 Intermediate Status:
% 32.68/33.07 Generated: 137403
% 32.68/33.07 Kept: 60573
% 32.68/33.07 Inuse: 892
% 89.87/90.41 Deleted: 1291
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying clauses:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 147086
% 89.87/90.41 Kept: 63128
% 89.87/90.41 Inuse: 907
% 89.87/90.41 Deleted: 1352
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 *** allocated 1946160 integers for termspace/termends
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 152306
% 89.87/90.41 Kept: 65158
% 89.87/90.41 Inuse: 927
% 89.87/90.41 Deleted: 1352
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 *** allocated 4378860 integers for clauses
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 156675
% 89.87/90.41 Kept: 67919
% 89.87/90.41 Inuse: 937
% 89.87/90.41 Deleted: 1352
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 163115
% 89.87/90.41 Kept: 71001
% 89.87/90.41 Inuse: 957
% 89.87/90.41 Deleted: 1352
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 168854
% 89.87/90.41 Kept: 73046
% 89.87/90.41 Inuse: 967
% 89.87/90.41 Deleted: 1352
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 174572
% 89.87/90.41 Kept: 75058
% 89.87/90.41 Inuse: 991
% 89.87/90.41 Deleted: 1352
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 184699
% 89.87/90.41 Kept: 78197
% 89.87/90.41 Inuse: 1004
% 89.87/90.41 Deleted: 1352
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 189948
% 89.87/90.41 Kept: 80606
% 89.87/90.41 Inuse: 1022
% 89.87/90.41 Deleted: 1352
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying clauses:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 199987
% 89.87/90.41 Kept: 86456
% 89.87/90.41 Inuse: 1052
% 89.87/90.41 Deleted: 2423
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 207453
% 89.87/90.41 Kept: 91467
% 89.87/90.41 Inuse: 1067
% 89.87/90.41 Deleted: 2423
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 219201
% 89.87/90.41 Kept: 94971
% 89.87/90.41 Inuse: 1097
% 89.87/90.41 Deleted: 2423
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 *** allocated 2919240 integers for termspace/termends
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 229897
% 89.87/90.41 Kept: 98100
% 89.87/90.41 Inuse: 1112
% 89.87/90.41 Deleted: 2423
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 *** allocated 6568290 integers for clauses
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 235659
% 89.87/90.41 Kept: 100596
% 89.87/90.41 Inuse: 1127
% 89.87/90.41 Deleted: 2423
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying clauses:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 241001
% 89.87/90.41 Kept: 102631
% 89.87/90.41 Inuse: 1152
% 89.87/90.41 Deleted: 2452
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 246519
% 89.87/90.41 Kept: 104708
% 89.87/90.41 Inuse: 1167
% 89.87/90.41 Deleted: 2452
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 251503
% 89.87/90.41 Kept: 107743
% 89.87/90.41 Inuse: 1177
% 89.87/90.41 Deleted: 2452
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 256612
% 89.87/90.41 Kept: 110788
% 89.87/90.41 Inuse: 1187
% 89.87/90.41 Deleted: 2452
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 261659
% 89.87/90.41 Kept: 112795
% 89.87/90.41 Inuse: 1210
% 89.87/90.41 Deleted: 2452
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 270465
% 89.87/90.41 Kept: 115813
% 89.87/90.41 Inuse: 1237
% 89.87/90.41 Deleted: 2452
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 276156
% 89.87/90.41 Kept: 117851
% 89.87/90.41 Inuse: 1262
% 89.87/90.41 Deleted: 2452
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 282733
% 89.87/90.41 Kept: 119859
% 89.87/90.41 Inuse: 1293
% 89.87/90.41 Deleted: 2453
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41 Resimplifying clauses:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 295760
% 89.87/90.41 Kept: 122028
% 89.87/90.41 Inuse: 1306
% 89.87/90.41 Deleted: 2571
% 89.87/90.41 Deletedinuse: 6
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 89.87/90.41 Generated: 303402
% 89.87/90.41 Kept: 124082
% 89.87/90.41 Inuse: 1316
% 89.87/90.41 Deleted: 2572
% 89.87/90.41 Deletedinuse: 7
% 89.87/90.41
% 89.87/90.41 Resimplifying inuse:
% 89.87/90.41 Done
% 89.87/90.41
% 89.87/90.41
% 89.87/90.41 Intermediate Status:
% 204.46/204.99 Generated: 310940
% 204.46/204.99 Kept: 126278
% 204.46/204.99 Inuse: 1326
% 204.46/204.99 Deleted: 2572
% 204.46/204.99 Deletedinuse: 7
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 319824
% 204.46/204.99 Kept: 129465
% 204.46/204.99 Inuse: 1346
% 204.46/204.99 Deleted: 2572
% 204.46/204.99 Deletedinuse: 7
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 325074
% 204.46/204.99 Kept: 131641
% 204.46/204.99 Inuse: 1361
% 204.46/204.99 Deleted: 2572
% 204.46/204.99 Deletedinuse: 7
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 330157
% 204.46/204.99 Kept: 133704
% 204.46/204.99 Inuse: 1376
% 204.46/204.99 Deleted: 2572
% 204.46/204.99 Deletedinuse: 7
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 *** allocated 4378860 integers for termspace/termends
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 347821
% 204.46/204.99 Kept: 136727
% 204.46/204.99 Inuse: 1391
% 204.46/204.99 Deleted: 2572
% 204.46/204.99 Deletedinuse: 7
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 361478
% 204.46/204.99 Kept: 139188
% 204.46/204.99 Inuse: 1406
% 204.46/204.99 Deleted: 2572
% 204.46/204.99 Deletedinuse: 7
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 368959
% 204.46/204.99 Kept: 141271
% 204.46/204.99 Inuse: 1426
% 204.46/204.99 Deleted: 2572
% 204.46/204.99 Deletedinuse: 7
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 378458
% 204.46/204.99 Kept: 146030
% 204.46/204.99 Inuse: 1431
% 204.46/204.99 Deleted: 2572
% 204.46/204.99 Deletedinuse: 7
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying clauses:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 *** allocated 9852435 integers for clauses
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 390123
% 204.46/204.99 Kept: 151600
% 204.46/204.99 Inuse: 1446
% 204.46/204.99 Deleted: 2791
% 204.46/204.99 Deletedinuse: 7
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 398241
% 204.46/204.99 Kept: 156237
% 204.46/204.99 Inuse: 1466
% 204.46/204.99 Deleted: 2792
% 204.46/204.99 Deletedinuse: 8
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 406422
% 204.46/204.99 Kept: 158337
% 204.46/204.99 Inuse: 1476
% 204.46/204.99 Deleted: 2793
% 204.46/204.99 Deletedinuse: 9
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 413809
% 204.46/204.99 Kept: 160368
% 204.46/204.99 Inuse: 1494
% 204.46/204.99 Deleted: 2793
% 204.46/204.99 Deletedinuse: 9
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 419227
% 204.46/204.99 Kept: 162397
% 204.46/204.99 Inuse: 1498
% 204.46/204.99 Deleted: 2793
% 204.46/204.99 Deletedinuse: 9
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 425424
% 204.46/204.99 Kept: 164403
% 204.46/204.99 Inuse: 1512
% 204.46/204.99 Deleted: 2793
% 204.46/204.99 Deletedinuse: 9
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying clauses:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 436229
% 204.46/204.99 Kept: 167730
% 204.46/204.99 Inuse: 1531
% 204.46/204.99 Deleted: 2891
% 204.46/204.99 Deletedinuse: 9
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 446665
% 204.46/204.99 Kept: 169769
% 204.46/204.99 Inuse: 1539
% 204.46/204.99 Deleted: 2892
% 204.46/204.99 Deletedinuse: 10
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 460069
% 204.46/204.99 Kept: 171949
% 204.46/204.99 Inuse: 1546
% 204.46/204.99 Deleted: 2892
% 204.46/204.99 Deletedinuse: 10
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 467274
% 204.46/204.99 Kept: 174398
% 204.46/204.99 Inuse: 1561
% 204.46/204.99 Deleted: 2892
% 204.46/204.99 Deletedinuse: 10
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 478737
% 204.46/204.99 Kept: 177793
% 204.46/204.99 Inuse: 1576
% 204.46/204.99 Deleted: 2892
% 204.46/204.99 Deletedinuse: 10
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 486689
% 204.46/204.99 Kept: 179953
% 204.46/204.99 Inuse: 1591
% 204.46/204.99 Deleted: 2892
% 204.46/204.99 Deletedinuse: 10
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 494827
% 204.46/204.99 Kept: 181955
% 204.46/204.99 Inuse: 1607
% 204.46/204.99 Deleted: 2892
% 204.46/204.99 Deletedinuse: 10
% 204.46/204.99
% 204.46/204.99 *** allocated 6568290 integers for termspace/termends
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 502398
% 204.46/204.99 Kept: 184459
% 204.46/204.99 Inuse: 1611
% 204.46/204.99 Deleted: 2892
% 204.46/204.99 Deletedinuse: 10
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 510034
% 204.46/204.99 Kept: 186795
% 204.46/204.99 Inuse: 1616
% 204.46/204.99 Deleted: 2892
% 204.46/204.99 Deletedinuse: 10
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying clauses:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99 Resimplifying inuse:
% 204.46/204.99 Done
% 204.46/204.99
% 204.46/204.99
% 204.46/204.99 Intermediate Status:
% 204.46/204.99 Generated: 527523
% 204.46/204.99 Kept: 191652
% 204.46/204.99 Inuse: 1631
% 204.46/204.99 Deleted: 3093
% 204.46/204.99 Deletedinuse: 10
% 300.07/300.58 Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------