TSTP Solution File: SWW235+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW235+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 23:21:27 EDT 2022
% Result : Timeout 300.01s 300.38s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW235+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n028.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 : Mon Jun 6 02:53:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.94/1.54 *** allocated 10000 integers for termspace/termends
% 0.94/1.54 *** allocated 10000 integers for clauses
% 0.94/1.54 *** allocated 10000 integers for justifications
% 0.94/1.54 *** allocated 15000 integers for termspace/termends
% 0.94/1.54 *** allocated 22500 integers for termspace/termends
% 0.94/1.54 *** allocated 33750 integers for termspace/termends
% 0.94/1.54 Bliksem 1.12
% 0.94/1.54
% 0.94/1.54
% 0.94/1.54 Automatic Strategy Selection
% 0.94/1.54
% 0.94/1.54 *** allocated 50625 integers for termspace/termends
% 0.94/1.54 *** allocated 75937 integers for termspace/termends
% 0.94/1.54 *** allocated 113905 integers for termspace/termends
% 0.94/1.54
% 0.94/1.54 Clauses:
% 0.94/1.54
% 0.94/1.54 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.94/1.54 { ! v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.94/1.54 tc_Complex_Ocomplex ) ) }.
% 0.94/1.54 { ! c_Polynomial_OpCons( tc_Complex_Ocomplex, v_c____, v_cs____ ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.94/1.54 }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, v_r____,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_z____ ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, v_da____,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.54 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), v_z____ ) ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.54 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), v_z____ ) ) ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.54 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), v_z____ ) ), v_aa____ ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ) ) }.
% 0.94/1.54 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.94/1.54 tc_Complex_Ocomplex ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.54 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, v_da____,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.54 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), v_z____ ) ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_z____ ) ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, v_r____,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, v_da____,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.54 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), X ) ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.94/1.54 , Y ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.94/1.54 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.94/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.94/1.54 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.94/1.54 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.54 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.94/1.54 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.94/1.54 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, v_da____,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ), hAPP
% 0.94/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_z____ ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.54 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), v_z____ ) ) ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, v_da____,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ), hAPP
% 0.94/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.54 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), v_z____ ) ) ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.94/1.54 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.94/1.54 v_r____ ) ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.54 v_z____ ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.94/1.54 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.94/1.54 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_Polynomial_Opoly( X ) ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.54 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.54 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.94/1.54 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.94/1.54 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.94/1.54 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.94/1.54 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.54 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.94/1.54 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.94/1.54 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.54 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.54 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.94/1.54 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.54 ( X, Y ) ) ) }.
% 0.94/1.54 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.94/1.54 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.54 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.94/1.54 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.54 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.54 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.54 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.94/1.54 ( X, T, Y ) ) ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.54 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.54 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.54 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.54 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.54 ( X, Y ) ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.54 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.54 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.94/1.54 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.54 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.94/1.54 hAPP( Y, U ) ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.94/1.54 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.54 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.54 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.94/1.54 hAPP( Y, U ) ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.94/1.54 ( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.94/1.54 ( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.54 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.94/1.54 hAPP( Y, U ) ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.94/1.54 ( Z, skol2( X, Y, Z ) ), hAPP( Y, skol2( X, Y, Z ) ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.94/1.54 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.94/1.54 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.94/1.54 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.94/1.54 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.94/1.54 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.94/1.54 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.94/1.54 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.94/1.54 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.94/1.54 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.94/1.54 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.94/1.54 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.54 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.94/1.54 ( X, Y, Z ) ) }.
% 0.94/1.54 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.94/1.54 tc_Complex_Ocomplex ) ), ! c_Orderings_Oord__class_Oless__eq(
% 0.94/1.54 tc_RealDef_Oreal, skol3( X, Y ), c_RealVector_Onorm__class_Onorm(
% 0.94/1.54 tc_Complex_Ocomplex, Z ) ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.54 tc_RealDef_Oreal, Y, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.94/1.54 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.54 tc_Complex_Ocomplex, X, v_cs____ ) ), Z ) ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.94/1.54 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.94/1.54 ), Y ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, skol4,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, v_da____,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.54 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), X ) ) ) }.
% 0.94/1.54 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.94/1.54 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.94/1.54 .
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.94/1.54 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.54 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.94/1.54 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.94/1.54 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.54 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.94/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.94/1.54 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.94/1.54 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.94/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.54 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.94/1.54 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.94/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.94/1.54 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.94/1.54 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.94/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.94/1.54 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.94/1.54 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.94/1.54 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.54 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.94/1.54 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.54 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.94/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.94/1.54 ) ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.54 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.54 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring__abs( X ), alpha53( X, Z ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring__abs( X ), alpha53( X, Z ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.54 { ! alpha53( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.54 { ! alpha53( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ), alpha53( X, Y ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.94/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.94/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.94/1.54 }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.54 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.94/1.54 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.54 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.54 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.94/1.54 ) ), T ), Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.94/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.94/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.54 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha1( X, Y
% 0.94/1.54 , Z ), alpha18( X, Y, Z ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), alpha18( X, Y, Z ) }.
% 0.94/1.54 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.54 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ), alpha1( X, Y, Z ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ), alpha2( X, Y, Z ), alpha19( X, Y, Z ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ) }.
% 0.94/1.54 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ), Y ), alpha19( X, Y, Z ) }.
% 0.94/1.54 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.54 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), alpha2( X, Y, Z ) }.
% 0.94/1.54 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semidom( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.54 Z ) ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.54 W ) ), U ), Y ) }.
% 0.94/1.54 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.54 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.54 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), Z ), U ), Y ) }.
% 0.94/1.54 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.94/1.54 Z ) ), U ), T ) = Y }.
% 0.94/1.54 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.94/1.54 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), Z ), U ), Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.94/1.54 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.94/1.54 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.94/1.54 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.94/1.54 Y ) ) ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.54 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.94/1.54 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.54 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.94/1.54 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.54 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.94/1.54 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.94/1.54 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.54 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 T, Y ), Z = Y }.
% 0.94/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 T, Y ) }.
% 0.94/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Y, Z ), T = Y }.
% 0.94/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Y, Z ) }.
% 0.94/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 T, Y ), Z = Y }.
% 0.94/1.54 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 T, Y ), Z = Y }.
% 0.94/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Y, T ), Z = Y }.
% 0.94/1.54 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.94/1.54 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.94/1.54 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.94/1.54 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.94/1.54 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.54 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.94/1.54 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.94/1.54 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.54 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.94/1.54 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.54 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.54 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.54 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.54 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.54 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.54 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.54 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.54 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.54 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.54 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.54 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.54 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.94/1.54 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.94/1.54 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.94/1.54 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.94/1.54 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.94/1.54 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.94/1.54 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.94/1.54 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.94/1.54 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.94/1.54 = Y }.
% 0.94/1.54 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.94/1.54 = Y }.
% 0.94/1.54 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.54 = Y }.
% 0.94/1.54 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.54 = Y }.
% 0.94/1.54 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.94/1.54 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.54 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.94/1.54 ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.94/1.54 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.94/1.54 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.54 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.94/1.54 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.94/1.54 .
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.94/1.54 .
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.94/1.54 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Y, Z ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Z, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.94/1.54 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.94/1.54 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.54 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.94/1.54 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.54 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.54 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.54 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.54 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.94/1.54 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.94/1.54 = Y }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.54 = Y }.
% 0.94/1.54 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.54 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.94/1.54 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.54 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.94/1.54 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.54 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.54 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.94/1.54 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.94/1.54 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.54 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.54 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.94/1.54 ), ! U = T }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.94/1.54 ), ! Z = Y }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.54 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.94/1.54 ) ), Z ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.94/1.54 ), U = Z, T = Y }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), !
% 0.94/1.54 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_Polynomial_Opoly( X ) ),
% 0.94/1.54 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.54 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.94/1.54 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.94/1.54 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol5( Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol5( X ) ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol6( Z, T ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol6( X, Y ) ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7( Z, T ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol7( X, Y ) ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.94/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.94/1.54 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.54 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.54 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.94/1.54 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.94/1.54 , Y ), X ) }.
% 0.94/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol8( X, Y ) ) }.
% 0.94/1.54 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol9( X, Y ) ) }.
% 0.94/1.54 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.54 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.94/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.94/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.54 tc_Nat_Onat, Z, Y ), X ) }.
% 0.94/1.54 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.94/1.54 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.54 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.94/1.54 tc_Nat_Onat ) }.
% 0.94/1.54 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ) }.
% 0.94/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.94/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.55 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.94/1.55 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.94/1.55 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Z, X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.94/1.55 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.94/1.55 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.94/1.55 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.94/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), X ) = X }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ) ) = X }.
% 0.94/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.94/1.55 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.94/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.94/1.55 .
% 0.94/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.94/1.55 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.94/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.94/1.55 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.94/1.55 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.94/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.94/1.55 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.94/1.55 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.94/1.55 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.94/1.55 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.94/1.55 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.94/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.94/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.94/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.94/1.55 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.55 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 0.94/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.55 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol10( X ) ) ) }.
% 0.94/1.55 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.94/1.55 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.94/1.55 ), c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.55 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.55 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.94/1.55 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.94/1.55 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.55 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.94/1.55 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.55 }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.94/1.55 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.94/1.55 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.94/1.55 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.94/1.55 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.94/1.55 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol11( X, Y ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol12( X, Y ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.94/1.55 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.94/1.55 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_RComplete_Onatfloor( X ), Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.94/1.55 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.94/1.55 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.94/1.55 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.55 Y ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 Y ), ! Z = Y }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.55 Z ), ! Z = Y }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.55 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.55 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.55 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.55 , ! Z = Y }.
% 0.94/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.55 , ! Z = Y }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.55 , ! Y = Z }.
% 0.94/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.55 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.94/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.94/1.55 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.55 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.55 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.55 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.94/1.55 Y = X }.
% 0.94/1.55 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.94/1.55 , X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, Y, Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.94/1.55 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.94/1.55 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.55 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.55 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.55 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.55 , ! Z = Y }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.55 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.55 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.94/1.55 ( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.55 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.55 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.55 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.55 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.55 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.55 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.55 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, Z, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, Z, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.55 , T ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , T, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , Y, T ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, Z, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , T, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, T, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , Y, Z ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.94/1.55 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 0.94/1.55 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.94/1.55 , X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.94/1.55 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.94/1.55 ) }.
% 0.94/1.55 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.94/1.55 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_RealDef_Oreal ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.55 , X ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_RealDef_Oreal ) ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 0.94/1.55 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.94/1.55 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.94/1.55 c_RComplete_Onatfloor( X ) = Y }.
% 0.94/1.55 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.94/1.55 ( tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.55 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.55 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.55 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha3( X, Y, Z, T ),
% 0.94/1.55 alpha20( X, Y, Z, T ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.55 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.55 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha20( X, Y, Z, T ) }.
% 0.94/1.55 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.94/1.55 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.94/1.55 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha3( X, Y, Z, T ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha4( X, Y, Z, T ),
% 0.94/1.55 alpha21( X, Y, Z, T ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha21( X, Y, Z, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.55 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha21( X, Y, Z, T ) }.
% 0.94/1.55 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.55 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.55 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha4( X, Y, Z, T ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.55 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ) }.
% 0.94/1.55 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.94/1.55 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.94/1.55 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , Y, T ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.94/1.55 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.55 .
% 0.94/1.55 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.94/1.55 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Nat_Onat ), X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.94/1.55 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.94/1.55 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 Y ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Z, X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.94/1.55 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.55 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.55 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.94/1.55 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( X, Z, W ) ), U ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.55 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.55 X, W, Z ) ), U ), T ), Y ) }.
% 0.94/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), Z ), U ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 0.94/1.55 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.94/1.55 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.94/1.55 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( X, Z, Y ), T ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.94/1.55 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( X, Z, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.94/1.55 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.55 , c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.94/1.55 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_RComplete_Onatceiling( Y ), X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.94/1.55 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.94/1.55 ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.94/1.55 ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.55 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.94/1.55 , ! alpha5( X, Y, Z ) }.
% 0.94/1.55 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.94/1.55 , ! alpha22( X, Y, Z ) }.
% 0.94/1.55 { alpha5( X, Y, Z ), alpha22( X, Y, Z ), hBOOL( hAPP( Z,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.55 { ! alpha22( X, Y, Z ), ! hBOOL( hAPP( Z, skol13( T, U, Z ) ) ) }.
% 0.94/1.55 { ! alpha22( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.94/1.55 skol13( X, Y, Z ) ) }.
% 0.94/1.55 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.94/1.55 ) ), alpha22( X, Y, Z ) }.
% 0.94/1.55 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.94/1.55 .
% 0.94/1.55 { ! alpha5( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha5( X, Y, Z ) }.
% 0.94/1.55 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.94/1.55 , alpha6( X, Y, Z ) }.
% 0.94/1.55 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.94/1.55 , alpha23( X, Y, Z ) }.
% 0.94/1.55 { ! alpha6( X, Y, Z ), ! alpha23( X, Y, Z ), hBOOL( hAPP( Z,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.55 { ! alpha23( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.94/1.55 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.55 { ! hBOOL( hAPP( Z, skol14( T, U, Z ) ) ), alpha23( X, Y, Z ) }.
% 0.94/1.55 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol14( X, Y, Z ) ),
% 0.94/1.55 alpha23( X, Y, Z ) }.
% 0.94/1.55 { ! alpha6( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.94/1.55 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha6( X, Y, Z ) }.
% 0.94/1.55 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6
% 0.94/1.55 ( X, Y, Z ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.94/1.55 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.94/1.55 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.55 , X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.94/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.55 , c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.94/1.55 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_RComplete_Onatceiling( X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.55 c_RComplete_Onatfloor( X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.55 c_RComplete_Onatceiling( X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.94/1.55 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.94/1.55 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.94/1.55 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.94/1.55 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.94/1.55 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.94/1.55 ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.94/1.55 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha7
% 0.94/1.55 ( X, Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.94/1.55 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! alpha7( X, Y, Z ),
% 0.94/1.55 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.94/1.55 { ! alpha7( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.94/1.55 ( X ) ) }.
% 0.94/1.55 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.55 alpha7( X, Y, Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol15( X ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, skol15( X ) ) ) }.
% 0.94/1.55 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 0.94/1.55 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol16( Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol16( X ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.94/1.55 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.94/1.55 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.94/1.55 { alpha54( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.94/1.55 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.94/1.55 { alpha54( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.94/1.55 ( X, Y ), Z ) ) }.
% 0.94/1.55 { ! alpha54( X, Y, Z ), alpha59( X, Y, Z ), Z = Y }.
% 0.94/1.55 { ! alpha54( X, Y, Z ), alpha59( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! alpha59( X, Y, Z ), alpha54( X, Y, Z ) }.
% 0.94/1.55 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha54( X, Y, Z ) }.
% 0.94/1.55 { ! alpha59( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.94/1.55 }.
% 0.94/1.55 { ! alpha59( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.94/1.55 X, Y ), Z ) ), alpha59( X, Y, Z ) }.
% 0.94/1.55 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.55 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.94/1.55 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.94/1.55 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.55 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol17( Z, T ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol17( X, Y ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol18( Z, T ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol18( X, Y ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol19( T, U, W ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ), skol19( X,
% 0.94/1.55 Y, Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), T ), hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), Z ) ) ), X ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol20( Z, T ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol20( X, Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol21( T, U, W ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol21( X, Y,
% 0.94/1.55 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, T ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol21( X, Y,
% 0.94/1.55 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, T, Z ) }.
% 0.94/1.55 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.94/1.55 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol22( Z, Y
% 0.94/1.55 ), Y ) }.
% 0.94/1.55 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.94/1.55 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.55 skol22( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.94/1.55 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.94/1.55 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.94/1.55 , skol22( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol23( T, U, W ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol23( X, Y,
% 0.94/1.55 Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, T ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol23( X, Y,
% 0.94/1.55 Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, T, Z ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, T, skol24( X, U, W, T ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.94/1.55 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.94/1.55 hAPP( Z, T ), hAPP( Z, skol24( X, Y, Z, T ) ) ) ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.94/1.55 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, skol25( X, Y ) ) ), X ) ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.55 tc_Nat_Onat, skol26( X, Y ), skol65( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 hAPP( Y, skol65( X, Y ) ), hAPP( Y, skol26( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.94/1.55 , Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.55 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol27( Z, T ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol27( X, Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol66( X, Y, Z ) ) ), Z ),
% 0.94/1.55 c_SEQ_OBseq( X, Y ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.94/1.55 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.94/1.55 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.94/1.55 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ) ) = Y }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Z, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.94/1.55 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.94/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.94/1.55 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.55 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.94/1.55 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.94/1.55 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.94/1.55 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.94/1.55 ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.94/1.55 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.94/1.55 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.94/1.55 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.94/1.55 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.94/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.55 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.55 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.94/1.55 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.94/1.55 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.55 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.94/1.55 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.94/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.55 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.94/1.55 ( tc_Nat_Onat ) ) ) ) }.
% 0.94/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.55 = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.94/1.55 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ) ) = Y }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.94/1.55 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.94/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.94/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.94/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.94/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.94/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.94/1.55 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.94/1.55 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.94/1.55 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.55 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.94/1.55 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.94/1.55 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.94/1.55 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.94/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol28( X, Y ) ), Y
% 0.94/1.55 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.94/1.55 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.94/1.55 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Y ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.94/1.55 ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.94/1.55 tc_Int_Oint, Y ) ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.94/1.55 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.94/1.55 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.94/1.55 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.94/1.55 }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.94/1.55 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.94/1.55 ( tc_Int_Oint ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.94/1.55 = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ) ) }.
% 0.94/1.55 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.94/1.55 }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.94/1.55 .
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ) ) = X }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), X ) = X }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.94/1.55 ( tc_Int_Oint ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.94/1.55 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.94/1.55 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.55 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.94/1.55 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.94/1.55 ( tc_Int_Oint ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.55 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.55 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.55 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.94/1.55 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, X, Y ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.94/1.55 tc_Int_Oint, X, Y ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.94/1.55 ) }.
% 0.94/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.94/1.55 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( Z, T ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol29( X, Y ) ) }.
% 0.94/1.55 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Orcis( Y
% 0.94/1.55 , X ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 0.94/1.55 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.94/1.55 ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.55 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.94/1.55 tc_Int_Oint, X, Y ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol30( X, Y, Z ) ) ), Y ),
% 0.94/1.55 c_SEQ_OBseq( X, Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol31( Z, Y ) ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.94/1.55 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.94/1.55 tc_Int_Oint, skol31( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.55 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.94/1.55 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.94/1.55 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.94/1.55 , Z ), X ) ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol32( Z, Y ) ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.94/1.55 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, skol32( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.55 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.94/1.55 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.94/1.55 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol33( Z, T ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol33( X, Y ) ), X ) =
% 0.94/1.55 Y }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol34( Z, T ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol34( X, Y ) ), X ) =
% 0.94/1.55 Y }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.94/1.55 skol34( X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.55 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.94/1.55 ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.55 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! X = Y,
% 0.94/1.55 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.94/1.55 ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_RealDef_Oreal, X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.94/1.55 ), c_Transcendental_Oln( Y ) ) }.
% 0.94/1.55 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.94/1.55 ( X ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.55 tc_RealDef_Oreal, X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.94/1.55 ( X ), c_Transcendental_Oln( Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.55 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.94/1.55 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.94/1.55 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.94/1.55 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.94/1.55 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! X =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.55 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.55 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.55 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.55 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_RealDef_Oreal ), X ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_RealDef_Oreal, c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.94/1.55 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) ), X ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.55 tc_Nat_Onat, skol35( X, Y ), skol67( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.94/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 hAPP( Y, skol35( X, Y ) ), hAPP( Y, skol67( X, Y ) ) ), c_SEQ_Oincseq( X
% 0.94/1.55 , Y ) }.
% 0.94/1.55 { alpha55( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol36( T, Y, U ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { alpha55( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ), hAPP(
% 0.94/1.55 X, skol36( X, Y, Z ) ) = Z }.
% 0.94/1.55 { ! alpha55( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol37( Z
% 0.94/1.55 , Y ), Y ) }.
% 0.94/1.55 { ! alpha55( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.94/1.55 tc_Int_Oint, hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, skol37( X
% 0.94/1.55 , Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, skol37( X,
% 0.94/1.55 Y ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.94/1.55 ( tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ) ) ), hAPP( X, Z ) ) ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ), alpha55( X, Y ) }.
% 0.94/1.55 { alpha56( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol38( T, Y, U ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { alpha56( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ), hAPP(
% 0.94/1.55 X, skol38( X, Y, Z ) ) = Z }.
% 0.94/1.55 { ! alpha56( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol39( Z
% 0.94/1.55 , Y ), Y ) }.
% 0.94/1.55 { ! alpha56( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.94/1.55 tc_Int_Oint, hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, skol39( X
% 0.94/1.55 , Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, skol39( X,
% 0.94/1.55 Y ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.94/1.55 ( tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ) ) ), hAPP( X, Z ) ) ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ), alpha56( X, Y ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol40( U, W, V0, T )
% 0.94/1.55 ), c_SEQ_OBseq( X, Y ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol40( X, Y, Z, T ) ) ), Z
% 0.94/1.55 ), c_SEQ_OBseq( X, Y ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol41( X, Y, Z ) ) ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, c_Nat_OSuc( skol68( X, Y ) ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol74( X, Y, Z ) ) ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol76( T, U ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol74( X, Y, Z ) ) ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol76( X, Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol42( X, Y, Z ) ) ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, c_Nat_OSuc( skol69( X, Y ) ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol75( X, Y, Z ) ) ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol77( T, U ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol75( X, Y, Z ) ) ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol77( X, Y ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.94/1.55 X ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.94/1.55 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.94/1.55 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.94/1.55 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.55 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.94/1.55 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.94/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.94/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.94/1.55 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.94/1.55 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.94/1.55 ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.94/1.55 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.94/1.55 X ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.94/1.55 .
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.94/1.55 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.94/1.55 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.94/1.55 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.94/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.94/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.94/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.94/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.94/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! X = c_Nat_OSuc( X ) }.
% 0.94/1.55 { ! c_Nat_OSuc( X ) = X }.
% 0.94/1.55 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.94/1.55 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.94/1.55 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.94/1.55 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.94/1.55 ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.94/1.55 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.94/1.55 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.55 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.94/1.55 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.94/1.55 ), X ) ) }.
% 0.94/1.55 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol43( X, Y ) ) ) }.
% 0.94/1.56 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.94/1.56 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.94/1.56 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.94/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha8( X, Y ), alpha24( X
% 0.94/1.56 , Y ) }.
% 0.94/1.56 { ! alpha8( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! alpha24( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! alpha24( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! alpha24( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha24( X, Y ) }.
% 0.94/1.56 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.94/1.56 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha9( X, Y ), alpha25
% 0.94/1.56 ( X, Y ) }.
% 0.94/1.56 { ! alpha9( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.56 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! alpha25( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.56 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! alpha25( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! alpha25( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha25( X, Y ) }.
% 0.94/1.56 { ! alpha9( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! alpha9( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol44( X ) ) }.
% 0.94/1.56 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.56 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.56 c_Nat_OSuc( X ) ) }.
% 0.94/1.56 { ! alpha10( X, Y ), Y = c_Nat_OSuc( skol45( Z, Y ) ) }.
% 0.94/1.56 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol45( X
% 0.94/1.56 , Y ), X ) }.
% 0.94/1.56 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.94/1.56 ), alpha10( X, Y ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.94/1.56 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.94/1.56 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.94/1.56 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.94/1.56 .
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.56 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.56 , c_Nat_OSuc( X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.94/1.56 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.94/1.56 }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.94/1.56 c_Nat_OSuc( X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.94/1.56 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.94/1.56 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.94/1.56 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), Y ), Z = Y }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.94/1.56 ) ) = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.94/1.56 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.56 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.94/1.56 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.94/1.56 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, c_Nat_OSuc( skol46( X, Y ) ) ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol70( X, Y, Z ) ) ),
% 0.94/1.56 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, c_Nat_OSuc( skol47( X, Y ) ) ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol71( X, Y, Z ) ) ),
% 0.94/1.56 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.94/1.56 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, skol48( X, Y ) ) ), X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, c_Nat_OSuc( skol48( X, Y ) ) ) ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.94/1.56 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha11( X, Y ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { ! alpha11( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { ! alpha11( X, Y ), alpha26( X, Y ), alpha33( X, Y ) }.
% 0.94/1.56 { ! alpha26( X, Y ), alpha11( X, Y ) }.
% 0.94/1.56 { ! alpha33( X, Y ), alpha11( X, Y ) }.
% 0.94/1.56 { ! alpha33( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! alpha33( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha33( X, Y ) }.
% 0.94/1.56 { ! alpha26( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! alpha26( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha26( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.94/1.56 , Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, X, Y ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Z, Y ), X ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.94/1.56 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.94/1.56 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.94/1.56 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.94/1.56 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.94/1.56 alpha12( X, Z ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.94/1.56 alpha27( X, Y, Z ) }.
% 0.94/1.56 { ! alpha12( X, Z ), ! alpha27( X, Y, Z ), hBOOL( hAPP( Z,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.94/1.56 { ! alpha27( X, Y, Z ), alpha34( X, Y, Z ) }.
% 0.94/1.56 { ! alpha27( X, Y, Z ), alpha38( X, Y, Z ) }.
% 0.94/1.56 { ! alpha34( X, Y, Z ), ! alpha38( X, Y, Z ), alpha27( X, Y, Z ) }.
% 0.94/1.56 { ! alpha38( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha43( X, Y, Z ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha38( X, Y, Z ) }.
% 0.94/1.56 { ! alpha43( X, Y, Z ), alpha38( X, Y, Z ) }.
% 0.94/1.56 { ! alpha43( X, Y, Z ), ! alpha47( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, skol49( T, U, Z ) ) ), alpha43( X, Y, Z ) }.
% 0.94/1.56 { alpha47( X, Y, skol49( X, Y, Z ) ), alpha43( X, Y, Z ) }.
% 0.94/1.56 { ! alpha47( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 skol50( X, T, U ) ) }.
% 0.94/1.56 { ! alpha47( X, Y, Z ), alpha51( X, Y, Z, skol50( X, Y, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha51( X, Y, Z
% 0.94/1.56 , T ), alpha47( X, Y, Z ) }.
% 0.94/1.56 { ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! alpha51( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha51( X,
% 0.94/1.56 Y, Z, T ) }.
% 0.94/1.56 { ! alpha34( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha39( X, Y, Z ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), X ), alpha34( X, Y, Z ) }.
% 0.94/1.56 { ! alpha39( X, Y, Z ), alpha34( X, Y, Z ) }.
% 0.94/1.56 { ! alpha39( X, Y, Z ), ! alpha44( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, skol51( T, U, Z ) ) ), alpha39( X, Y, Z ) }.
% 0.94/1.56 { alpha44( X, Y, skol51( X, Y, Z ) ), alpha39( X, Y, Z ) }.
% 0.94/1.56 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol52( T, U, W ) ) }.
% 0.94/1.56 { ! alpha44( X, Y, Z ), alpha48( X, Y, Z, skol52( X, Y, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha48( X, Y, Z, T )
% 0.94/1.56 , alpha44( X, Y, Z ) }.
% 0.94/1.56 { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! alpha48( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha48( X,
% 0.94/1.56 Y, Z, T ) }.
% 0.94/1.56 { ! alpha12( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.56 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha12( X, Y ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha12
% 0.94/1.56 ( X, Y ) }.
% 0.94/1.56 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha57( X,
% 0.94/1.56 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, T, Z ) = Y }.
% 0.94/1.56 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha57( X,
% 0.94/1.56 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, T, Z ) = Y }.
% 0.94/1.56 { ! alpha57( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! alpha57( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha57( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.94/1.56 , alpha57( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, skol53( X ) ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, c_Nat_OSuc( skol53( X ) ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha13( X, Y, T,
% 0.94/1.56 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha13( X, Y, skol54( X, Y
% 0.94/1.56 , Z ), skol72( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.94/1.56 skol54( X, Y, Z ) ), skol72( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.94/1.56 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.94/1.56 ) }.
% 0.94/1.56 { ! alpha13( X, Y, Z, T ), alpha28( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha28( X, Y, Z
% 0.94/1.56 , T ), alpha13( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha28( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! alpha28( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha28( X,
% 0.94/1.56 Y, Z, T ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ) ) = X }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.94/1.56 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.94/1.56 ), Y ) ) = Z }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 0.94/1.56 , Z ) ) = Y }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 0.94/1.56 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), X ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.94/1.56 ( X ), T, Z ), Y ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.94/1.56 X, Z, Y ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.94/1.56 ( X, Z, Y ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.94/1.56 ( X, Y, Z ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.94/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.94/1.56 , Y ) ), Y ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.94/1.56 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.94/1.56 ), Z ), Y ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.94/1.56 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.94/1.56 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.94/1.56 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 T, Z ), Y ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.94/1.56 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 T, Y ), Z ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.94/1.56 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.94/1.56 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.94/1.56 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.94/1.56 ), Z ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Int_Oint, Z, X ), Y ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Int_Oint, Z, Y ), X ) }.
% 0.94/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.94/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.94/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.94/1.56 Y ) ), Y ) }.
% 0.94/1.56 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.94/1.56 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.94/1.56 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.94/1.56 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.94/1.56 , U ), Z ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.94/1.56 , Y ) ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.94/1.56 ), Z ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.94/1.56 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.94/1.56 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.94/1.56 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol55( X, Y ) ) }.
% 0.94/1.56 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.94/1.56 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.94/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.94/1.56 ( tc_Int_Oint, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.94/1.56 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.94/1.56 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.94/1.56 }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.94/1.56 ( tc_Int_Oint, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.94/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.94/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.94/1.56 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.56 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 0.94/1.56 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.94/1.56 ( tc_Int_Oint, X, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.94/1.56 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.94/1.56 alpha14( X, Z ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.94/1.56 alpha29( X, Y, Z ) }.
% 0.94/1.56 { ! alpha14( X, Z ), ! alpha29( X, Y, Z ), hBOOL( hAPP( Z,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.56 { ! alpha29( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 alpha35( X, Y, Z ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha29( X, Y, Z ) }.
% 0.94/1.56 { ! alpha35( X, Y, Z ), alpha29( X, Y, Z ) }.
% 0.94/1.56 { ! alpha35( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.94/1.56 ), alpha40( X, Y, Z, T ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol56( X, T, U ), X ),
% 0.94/1.56 alpha35( X, Y, Z ) }.
% 0.94/1.56 { ! alpha40( X, Y, Z, skol56( X, Y, Z ) ), alpha35( X, Y, Z ) }.
% 0.94/1.56 { ! alpha40( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.94/1.56 hBOOL( hAPP( Z, U ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, skol57( U, W, Z, V0 ) ) ), alpha40( X, Y, Z, T ) }.
% 0.94/1.56 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol57( X, Y, Z, T ) )
% 0.94/1.56 , T ), alpha40( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha14( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha14( X, Y ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha14
% 0.94/1.56 ( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 0.94/1.56 ( tc_Int_Oint, X, Y ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y )
% 0.94/1.56 }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.94/1.56 alpha15( X, Z ), alpha30( X, Y, Z ) }.
% 0.94/1.56 { ! alpha15( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.56 { ! alpha30( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.56 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol58( X
% 0.94/1.56 , Y, T ) ), Y ) }.
% 0.94/1.56 { ! alpha30( X, Y, Z ), alpha36( X, Y, Z, skol58( X, Y, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ), Y ), ! alpha36( X
% 0.94/1.56 , Y, Z, T ), alpha30( X, Y, Z ) }.
% 0.94/1.56 { ! alpha36( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 0.94/1.56 ( T ) ) ) }.
% 0.94/1.56 { ! alpha36( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 0.94/1.56 hBOOL( hAPP( Z, T ) ), alpha36( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha15( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! alpha15( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ) ) ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha15( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ), Z
% 0.94/1.56 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.94/1.56 , Y ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.94/1.56 alpha16( X, Y, Z ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.94/1.56 alpha31( X, Y, Z ) }.
% 0.94/1.56 { ! alpha16( X, Y, Z ), ! alpha31( X, Y, Z ), hBOOL( hAPP( Z,
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.94/1.56 { ! alpha31( X, Y, Z ), alpha37( X, Y, Z ) }.
% 0.94/1.56 { ! alpha31( X, Y, Z ), alpha41( X, Y, Z ) }.
% 0.94/1.56 { ! alpha37( X, Y, Z ), ! alpha41( X, Y, Z ), alpha31( X, Y, Z ) }.
% 0.94/1.56 { ! alpha41( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha45( X, Y, Z ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha41( X, Y, Z ) }.
% 0.94/1.56 { ! alpha45( X, Y, Z ), alpha41( X, Y, Z ) }.
% 0.94/1.56 { ! alpha45( X, Y, Z ), ! alpha49( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, skol59( T, U, Z ) ) ), alpha45( X, Y, Z ) }.
% 0.94/1.56 { alpha49( X, Y, skol59( X, Y, Z ) ), alpha45( X, Y, Z ) }.
% 0.94/1.56 { ! alpha49( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z )
% 0.94/1.56 }.
% 0.94/1.56 { ! alpha49( X, Y, Z ), alpha52( X, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), ! alpha52( X, Y, Z
% 0.94/1.56 ), alpha49( X, Y, Z ) }.
% 0.94/1.56 { ! alpha52( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! alpha52( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol60( X, Y,
% 0.94/1.56 Z ) ), Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha52( X,
% 0.94/1.56 Y, Z ) }.
% 0.94/1.56 { ! alpha37( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha42( X, Y, Z ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), X ), alpha37( X, Y, Z ) }.
% 0.94/1.56 { ! alpha42( X, Y, Z ), alpha37( X, Y, Z ) }.
% 0.94/1.56 { ! alpha42( X, Y, Z ), ! alpha46( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, skol61( T, U, Z ) ) ), alpha42( X, Y, Z ) }.
% 0.94/1.56 { alpha46( X, Y, skol61( X, Y, Z ) ), alpha42( X, Y, Z ) }.
% 0.94/1.56 { ! alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 0.94/1.56 { ! alpha46( X, Y, Z ), alpha50( X, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! alpha50( X, Y, Z ),
% 0.94/1.56 alpha46( X, Y, Z ) }.
% 0.94/1.56 { ! alpha50( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X )
% 0.94/1.56 }.
% 0.94/1.56 { ! alpha50( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol62( X, Y,
% 0.94/1.56 Z ) ), Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! Y =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha50( X,
% 0.94/1.56 Y, Z ) }.
% 0.94/1.56 { ! alpha16( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.56 hBOOL( hAPP( Z, Y ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha16( X, Y, Z ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, Y ) ), alpha16( X, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.56 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.56 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha58( X,
% 0.94/1.56 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.94/1.56 tc_Int_Oint, Z, Y ) = X }.
% 0.94/1.56 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha58( X,
% 0.94/1.56 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.94/1.56 tc_Int_Oint, Z, Y ) = X }.
% 0.94/1.56 { ! alpha58( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! alpha58( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha58( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.94/1.56 , alpha58( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.94/1.56 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.94/1.56 ) ), ! alpha17( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), alpha17( X, Y, skol63( X, Y, Z ), skol73( X, Y, Z )
% 0.94/1.56 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.94/1.56 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol63( X, Y, Z ) ), skol73
% 0.94/1.56 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.94/1.56 { ! alpha17( X, Y, Z, T ), alpha32( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha32( X, Y, Z, T )
% 0.94/1.56 , alpha17( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! alpha32( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha32( X,
% 0.94/1.56 Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.94/1.56 c_RComplete_Onatfloor( X ), Y ) }.
% 0.94/1.56 { c_Complex_Ocis( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Y ) ) ), X
% 0.94/1.56 ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.56 c_Complex_Ocis( X ) ), c_Complex_Ocis( hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ) ), X ) ) ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.94/1.56 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ),
% 0.94/1.56 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.94/1.56 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ), Z ), c_Divides_Odiv__class_Omod(
% 0.94/1.56 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.94/1.56 ( X ), T, Z ), Y ) ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X
% 0.94/1.56 ), T, Z ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), X ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Divides_Odiv__class_Omod
% 0.94/1.56 ( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Y ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Divides_Odiv__class_Omod
% 0.94/1.56 ( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv
% 0.94/1.56 ( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Nat_Onat, X, Y ), Y ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.56 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol64( X, Y ) ) }.
% 0.94/1.56 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.94/1.56 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.94/1.56 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.94/1.56 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.94/1.56 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.94/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.56 tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.94/1.56 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.94/1.56 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.94/1.56 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.94/1.56 { class_Power_Opower( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.94/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.56 tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.94/1.56 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.94/1.56 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.94/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.56 tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.94/1.56 .
% 0.94/1.56 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.56 tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ),
% 0.94/1.56 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.94/1.56 X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.94/1.56 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.94/1.56 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.94/1.56 ( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.94/1.56 ( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.94/1.56 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), hAPP(
% 0.94/1.56 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.56 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), v_z____ ) ) ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.56 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.56 tc_Complex_Ocomplex, v_aa____, c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.94/1.56 v_c____, v_cs____ ) ) ), v_z____ ) ) ) }.
% 0.94/1.56
% 0.94/1.56 *** allocated 15000 integers for clauses
% 0.94/1.56 *** allocated 22500 integers for clauses
% 0.94/1.56 *** allocated 33750 integers for clauses
% 0.94/1.56 *** allocated 50625 integers for clauses
% 0.94/1.56 *** allocated 75937 integers for clauses
% 0.94/1.56 *** allocated 113905 integers for clauses
% 0.94/1.56 percentage equality = 0.238818, percentage horn = 0.915484
% 0.94/1.56 This is a problem with some equality
% 0.94/1.56
% 0.94/1.56
% 0.94/1.56
% 0.94/1.56 Options Used:
% 0.94/1.56
% 0.94/1.56 useres = 1
% 0.94/1.56 useparamod = 1
% 0.94/1.56 useeqrefl = 1
% 0.94/1.56 useeqfact = 1
% 0.94/1.56 usefactor = 1
% 0.94/1.56 usesimpsplitting = 0
% 0.94/1.56 usesimpdemod = 5
% 0.94/1.56 usesimpres = 3
% 0.94/1.56
% 0.94/1.56 resimpinuse = 1000
% 0.94/1.56 resimpclauses = 20000
% 0.94/1.56 substype = eqrewr
% 0.94/1.56 backwardsubs = 1
% 0.94/1.56 selectoldest = 5
% 0.94/1.56
% 0.94/1.56 litorderings [0] = split
% 0.94/1.56 litorderings [1] = extend the termordering, first sorting on arguments
% 0.94/1.56
% 0.94/1.56 termordering = kbo
% 0.94/1.56
% 0.94/1.56 litapriori = 0
% 0.94/1.56 termapriori = 1
% 0.94/1.56 litaposteriori = 0
% 0.94/1.56 termaposteriori = 0
% 0.94/1.56 demodaposteriori = 0
% 0.94/1.56 ordereqreflfact = 0
% 0.94/1.56
% 0.94/1.56 litselect = negord
% 0.94/1.56
% 0.94/1.56 maxweight = 15
% 0.94/1.56 maxdepth = 30000
% 0.94/1.56 maxlength = 115
% 0.94/1.56 maxnrvars = 195
% 0.94/1.56 excuselevel = 1
% 0.94/1.56 increasemaxweight = 1
% 0.94/1.56
% 0.94/1.56 maxselected = 10000000
% 0.94/1.56 maxnrclauses = 10000000
% 0.94/1.56
% 0.94/1.56 showgenerated = 0
% 0.94/1.56 showkept = 0
% 0.94/1.56 showselected = 0
% 0.94/1.56 showdeleted = 0
% 0.94/1.56 showresimp = 1
% 0.94/1.56 showstatus = 2000
% 0.94/1.56
% 0.94/1.56 prologoutput = 0
% 0.94/1.56 nrgoals = 5000000
% 0.94/1.56 totalproof = 1
% 0.94/1.56
% 0.94/1.56 Symbols occurring in the translation:
% 0.94/1.56
% 0.94/1.56 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.94/1.56 . [1, 2] (w:1, o:203, a:1, s:1, b:0),
% 0.94/1.56 ! [4, 1] (w:0, o:116, a:1, s:1, b:0),
% 0.94/1.56 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.56 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.56 hAPP [38, 2] (w:1, o:227, a:1, s:1, b:0),
% 0.94/1.56 v_cs____ [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.94/1.56 tc_Complex_Ocomplex [40, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.94/1.56 tc_Polynomial_Opoly [41, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.94/1.56 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.94/1.56 v_c____ [43, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.94/1.56 c_Polynomial_OpCons [44, 3] (w:1, o:298, a:1, s:1, b:0),
% 0.94/1.56 tc_RealDef_Oreal [45, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.94/1.56 v_r____ [46, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.94/1.56 v_z____ [47, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm [48, 2] (w:1, o:228, a:1, s:1, b:0),
% 0.94/1.56
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq [49, 3] (w:1, o:295, a:1, s:1, b:0)
% 0.94/1.56 ,
% 0.94/1.56 v_da____ [50, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.94/1.56 c_Groups_Otimes__class_Otimes [51, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.94/1.56 c_Polynomial_Opoly [52, 2] (w:1, o:229, a:1, s:1, b:0),
% 0.94/1.56 v_aa____ [53, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.94/1.56 c_Groups_Ominus__class_Ominus [54, 3] (w:1, o:299, a:1, s:1, b:0),
% 0.94/1.56 c_Groups_Oplus__class_Oplus [55, 3] (w:1, o:300, a:1, s:1, b:0),
% 0.94/1.56 v_p [56, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.94/1.56 class_RealVector_Oreal__normed__vector [60, 1] (w:1, o:130, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 c_Groups_Oone__class_Oone [61, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.94/1.56 class_RealVector_Oreal__normed__algebra [65, 1] (w:1, o:132, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Orderings_Opreorder [66, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Ocomm__ring [69, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Ocomm__semiring__0 [70, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Oab__group__add [71, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.94/1.56 c_Groups_Oabs__class_Oabs [72, 2] (w:1, o:231, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Ocomm__semiring__1 [73, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.94/1.56 class_RealVector_Oreal__normed__algebra__1 [74, 1] (w:1, o:142, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 class_Groups_Ozero [75, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Ocomm__monoid__add [79, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.94/1.56
% 0.94/1.56 class_Int_Oring__char__0 [84, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Oidom [85, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.94/1.56 class_Orderings_Olinorder [90, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.94/1.56 class_Orderings_Oord [92, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.94/1.56 tc_fun [93, 2] (w:1, o:269, a:1, s:1, b:0),
% 0.94/1.56 class_Orderings_Oorder [94, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.94/1.56 class_RealVector_Oreal__normed__div__algebra [98, 1] (w:1, o:148, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 class_Rings_Olinordered__semiring__1 [102, 1] (w:1, o:151, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Rings_Oring__1 [103, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Oordered__ring [107, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Olinordered__idom [108, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Olinordered__ring__strict [109, 1] (w:1, o:149, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Rings_Olinordered__ring [110, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Oordered__ring__abs [112, 1] (w:1, o:156, a:1, s:1, b:0)
% 0.94/1.56 ,
% 0.94/1.56 class_Rings_Omult__zero [119, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Oring__no__zero__divisors [120, 1] (w:1, o:163, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Rings_Ono__zero__divisors [121, 1] (w:1, o:153, a:1, s:1, b:0)
% 0.94/1.56 ,
% 0.94/1.56 class_Rings_Ozero__neq__one [122, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Ocomm__semiring [123, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Osemiring [125, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Oordered__cancel__semiring [126, 1] (w:1, o:169, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Rings_Oordered__semiring [127, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.94/1.56
% 0.94/1.56 class_Rings_Oordered__comm__semiring [128, 1] (w:1, o:171, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Rings_Olinordered__semidom [129, 1] (w:1, o:157, a:1, s:1, b:0)
% 0.94/1.56 ,
% 0.94/1.56 class_Rings_Oring [130, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Oordered__ab__group__add__abs [131, 1] (w:1, o:172, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 c_Polynomial_Opcompose [132, 3] (w:1, o:301, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Oab__semigroup__mult [133, 1] (w:1, o:173, a:1, s:1, b:0
% 0.94/1.56 ),
% 0.94/1.56 class_Groups_Oab__semigroup__add [134, 1] (w:1, o:174, a:1, s:1, b:0)
% 0.94/1.56 ,
% 0.94/1.56 class_Groups_Ocancel__semigroup__add [135, 1] (w:1, o:175, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Groups_Ocancel__ab__semigroup__add [136, 1] (w:1, o:176, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 class_Groups_Oone [137, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Omonoid__add [138, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Olinordered__ab__group__add [139, 1] (w:1, o:178, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 class_Groups_Oordered__ab__semigroup__add__imp__le [140, 1] (w:1, o:
% 0.94/1.56 180, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Oordered__ab__semigroup__add [141, 1] (w:1, o:181, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 class_Groups_Ogroup__add [142, 1] (w:1, o:182, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Oordered__ab__group__add [143, 1] (w:1, o:183, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Groups_Ocomm__monoid__mult [144, 1] (w:1, o:184, a:1, s:1, b:0)
% 0.94/1.56 ,
% 0.94/1.56 class_Groups_Omonoid__mult [145, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Oordered__comm__monoid__add [146, 1] (w:1, o:186, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.94/1.56 148, 1] (w:1, o:188, a:1, s:1, b:0),
% 0.94/1.56 c_Polynomial_Oorder [149, 3] (w:1, o:297, a:1, s:1, b:0),
% 0.94/1.56 tc_Nat_Onat [150, 0] (w:1, o:81, a:1, s:1, b:0),
% 0.94/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [158, 2] (w:1, o:
% 0.94/1.56 230, a:1, s:1, b:0),
% 0.94/1.56 c_Polynomial_Opoly__rec [159, 5] (w:1, o:383, a:1, s:1, b:0),
% 0.94/1.56 c_fequal [172, 2] (w:1, o:270, a:1, s:1, b:0),
% 0.94/1.56 c_If [173, 4] (w:1, o:367, a:1, s:1, b:0),
% 0.94/1.56 c_RComplete_Onatceiling [175, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.94/1.56 c_Complex_Oexpi [176, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.94/1.56 c_RComplete_Onatfloor [177, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.94/1.56 c_RealDef_Oreal [178, 2] (w:1, o:271, a:1, s:1, b:0),
% 0.94/1.56 c_Groups_Osgn__class_Osgn [179, 2] (w:1, o:272, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Olinordered__semiring__1__strict [180, 1] (w:1, o:158, a:
% 0.94/1.56 1, s:1, b:0),
% 0.94/1.56 c_Orderings_Oord__class_Oless [181, 3] (w:1, o:296, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Oordered__cancel__ab__semigroup__add [182, 1] (w:1, o:
% 0.94/1.56 192, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Osgn__if [183, 1] (w:1, o:193, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Olinordered__comm__semiring__strict [184, 1] (w:1, o:159
% 0.94/1.56 , a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Olinordered__semiring__strict [185, 1] (w:1, o:160, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 class_Rings_Olinordered__semiring [186, 1] (w:1, o:161, a:1, s:1, b:0
% 0.94/1.56 ),
% 0.94/1.56 hBOOL [190, 1] (w:1, o:194, a:1, s:1, b:0),
% 0.94/1.56 c_Polynomial_Opos__poly [192, 2] (w:1, o:273, a:1, s:1, b:0),
% 0.94/1.56 c_Complex_Oii [193, 0] (w:1, o:103, a:1, s:1, b:0),
% 0.94/1.56 c_SEQ_Odecseq [201, 2] (w:1, o:274, a:1, s:1, b:0),
% 0.94/1.56 c_Power_Opower__class_Opower [202, 1] (w:1, o:195, a:1, s:1, b:0),
% 0.94/1.56 c_SEQ_OBseq [203, 2] (w:1, o:275, a:1, s:1, b:0),
% 0.94/1.56 class_Power_Opower [204, 1] (w:1, o:196, a:1, s:1, b:0),
% 0.94/1.56 tc_Int_Oint [205, 0] (w:1, o:108, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Oring__1__no__zero__divisors [206, 1] (w:1, o:167, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 class_Rings_Osemiring__0 [207, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.94/1.56 c_Power_Opower_Opower [209, 3] (w:1, o:302, a:1, s:1, b:0),
% 0.94/1.57 c_Nat__Transfer_Otsub [216, 2] (w:1, o:276, a:1, s:1, b:0),
% 0.94/1.57 c_Complex_Orcis [217, 2] (w:1, o:277, a:1, s:1, b:0),
% 0.94/1.57 c_Transcendental_Oln [221, 1] (w:1, o:197, a:1, s:1, b:0),
% 0.94/1.57 c_SEQ_Oincseq [222, 2] (w:1, o:278, a:1, s:1, b:0),
% 0.94/1.57 c_Nat_OSuc [225, 1] (w:1, o:198, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Ocomm__ring__1 [231, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.94/1.57 c_Divides_Odiv__class_Odiv [232, 3] (w:1, o:303, a:1, s:1, b:0),
% 0.94/1.57 class_Divides_Osemiring__div [233, 1] (w:1, o:200, a:1, s:1, b:0),
% 0.94/1.57 c_Divides_Odiv__class_Omod [237, 3] (w:1, o:304, a:1, s:1, b:0),
% 0.94/1.57 class_Fields_Ofield [238, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.94/1.57 class_Divides_Oring__div [239, 1] (w:1, o:199, a:1, s:1, b:0),
% 0.94/1.57 c_Rings_Oinverse__class_Odivide [242, 3] (w:1, o:305, a:1, s:1, b:0)
% 0.94/1.57 ,
% 0.94/1.57 c_Complex_Ocis [243, 1] (w:1, o:201, a:1, s:1, b:0),
% 0.94/1.57 class_Groups_Ocancel__comm__monoid__add [245, 1] (w:1, o:202, a:1, s:
% 0.94/1.57 1, b:0),
% 0.94/1.57 tc_HOL_Obool [247, 0] (w:1, o:107, a:1, s:1, b:0),
% 0.94/1.57 alpha1 [248, 3] (w:1, o:306, a:1, s:1, b:1),
% 0.94/1.57 alpha2 [249, 3] (w:1, o:310, a:1, s:1, b:1),
% 0.94/1.57 alpha3 [250, 4] (w:1, o:371, a:1, s:1, b:1),
% 0.94/1.57 alpha4 [251, 4] (w:1, o:374, a:1, s:1, b:1),
% 0.94/1.57 alpha5 [252, 3] (w:1, o:319, a:1, s:1, b:1),
% 0.94/1.57 alpha6 [253, 3] (w:1, o:324, a:1, s:1, b:1),
% 0.94/1.57 alpha7 [254, 3] (w:1, o:325, a:1, s:1, b:1),
% 0.94/1.57 alpha8 [255, 2] (w:1, o:279, a:1, s:1, b:1),
% 0.94/1.57 alpha9 [256, 2] (w:1, o:280, a:1, s:1, b:1),
% 0.94/1.57 alpha10 [257, 2] (w:1, o:281, a:1, s:1, b:1),
% 0.94/1.57 alpha11 [258, 2] (w:1, o:282, a:1, s:1, b:1),
% 0.94/1.57 alpha12 [259, 2] (w:1, o:283, a:1, s:1, b:1),
% 0.94/1.57 alpha13 [260, 4] (w:1, o:375, a:1, s:1, b:1),
% 0.94/1.57 alpha14 [261, 2] (w:1, o:284, a:1, s:1, b:1),
% 0.94/1.57 alpha15 [262, 2] (w:1, o:285, a:1, s:1, b:1),
% 0.94/1.57 alpha16 [263, 3] (w:1, o:307, a:1, s:1, b:1),
% 0.94/1.57 alpha17 [264, 4] (w:1, o:376, a:1, s:1, b:1),
% 0.94/1.57 alpha18 [265, 3] (w:1, o:308, a:1, s:1, b:1),
% 0.94/1.57 alpha19 [266, 3] (w:1, o:309, a:1, s:1, b:1),
% 0.94/1.57 alpha20 [267, 4] (w:1, o:368, a:1, s:1, b:1),
% 0.94/1.57 alpha21 [268, 4] (w:1, o:369, a:1, s:1, b:1),
% 0.94/1.57 alpha22 [269, 3] (w:1, o:326, a:1, s:1, b:1),
% 0.94/1.57 alpha23 [270, 3] (w:1, o:327, a:1, s:1, b:1),
% 0.94/1.57 alpha24 [271, 2] (w:1, o:286, a:1, s:1, b:1),
% 0.94/1.57 alpha25 [272, 2] (w:1, o:287, a:1, s:1, b:1),
% 0.94/1.57 alpha26 [273, 2] (w:1, o:288, a:1, s:1, b:1),
% 0.94/1.57 alpha27 [274, 3] (w:1, o:328, a:1, s:1, b:1),
% 0.94/1.57 alpha28 [275, 4] (w:1, o:370, a:1, s:1, b:1),
% 0.94/1.57 alpha29 [276, 3] (w:1, o:329, a:1, s:1, b:1),
% 0.94/1.57 alpha30 [277, 3] (w:1, o:330, a:1, s:1, b:1),
% 0.94/1.57 alpha31 [278, 3] (w:1, o:331, a:1, s:1, b:1),
% 0.94/1.57 alpha32 [279, 4] (w:1, o:372, a:1, s:1, b:1),
% 0.94/1.57 alpha33 [280, 2] (w:1, o:289, a:1, s:1, b:1),
% 0.94/1.57 alpha34 [281, 3] (w:1, o:332, a:1, s:1, b:1),
% 0.94/1.57 alpha35 [282, 3] (w:1, o:333, a:1, s:1, b:1),
% 0.94/1.57 alpha36 [283, 4] (w:1, o:373, a:1, s:1, b:1),
% 0.94/1.57 alpha37 [284, 3] (w:1, o:334, a:1, s:1, b:1),
% 0.94/1.57 alpha38 [285, 3] (w:1, o:335, a:1, s:1, b:1),
% 0.94/1.57 alpha39 [286, 3] (w:1, o:336, a:1, s:1, b:1),
% 0.94/1.57 alpha40 [287, 4] (w:1, o:377, a:1, s:1, b:1),
% 0.94/1.57 alpha41 [288, 3] (w:1, o:311, a:1, s:1, b:1),
% 0.94/1.57 alpha42 [289, 3] (w:1, o:312, a:1, s:1, b:1),
% 0.94/1.57 alpha43 [290, 3] (w:1, o:313, a:1, s:1, b:1),
% 0.94/1.57 alpha44 [291, 3] (w:1, o:314, a:1, s:1, b:1),
% 0.94/1.57 alpha45 [292, 3] (w:1, o:315, a:1, s:1, b:1),
% 0.94/1.57 alpha46 [293, 3] (w:1, o:316, a:1, s:1, b:1),
% 0.94/1.57 alpha47 [294, 3] (w:1, o:317, a:1, s:1, b:1),
% 0.94/1.57 alpha48 [295, 4] (w:1, o:378, a:1, s:1, b:1),
% 0.94/1.57 alpha49 [296, 3] (w:1, o:318, a:1, s:1, b:1),
% 0.94/1.57 alpha50 [297, 3] (w:1, o:320, a:1, s:1, b:1),
% 0.94/1.57 alpha51 [298, 4] (w:1, o:379, a:1, s:1, b:1),
% 0.94/1.57 alpha52 [299, 3] (w:1, o:321, a:1, s:1, b:1),
% 0.94/1.57 alpha53 [300, 2] (w:1, o:290, a:1, s:1, b:1),
% 0.94/1.57 alpha54 [301, 3] (w:1, o:322, a:1, s:1, b:1),
% 0.94/1.57 alpha55 [302, 2] (w:1, o:291, a:1, s:1, b:1),
% 0.94/1.57 alpha56 [303, 2] (w:1, o:292, a:1, s:1, b:1),
% 0.94/1.57 alpha57 [304, 2] (w:1, o:293, a:1, s:1, b:1),
% 0.94/1.57 alpha58 [305, 2] (w:1, o:294, a:1, s:1, b:1),
% 11.13/11.54 alpha59 [306, 3] (w:1, o:323, a:1, s:1, b:1),
% 11.13/11.54 skol1 [307, 2] (w:1, o:232, a:1, s:1, b:1),
% 11.13/11.54 skol2 [308, 3] (w:1, o:340, a:1, s:1, b:1),
% 11.13/11.54 skol3 [309, 2] (w:1, o:240, a:1, s:1, b:1),
% 11.13/11.54 skol4 [310, 0] (w:1, o:14, a:1, s:1, b:1),
% 11.13/11.54 skol5 [311, 1] (w:1, o:122, a:1, s:1, b:1),
% 11.13/11.54 skol6 [312, 2] (w:1, o:242, a:1, s:1, b:1),
% 11.13/11.54 skol7 [313, 2] (w:1, o:248, a:1, s:1, b:1),
% 11.13/11.54 skol8 [314, 2] (w:1, o:251, a:1, s:1, b:1),
% 11.13/11.54 skol9 [315, 2] (w:1, o:252, a:1, s:1, b:1),
% 11.13/11.54 skol10 [316, 1] (w:1, o:123, a:1, s:1, b:1),
% 11.13/11.54 skol11 [317, 2] (w:1, o:253, a:1, s:1, b:1),
% 11.13/11.54 skol12 [318, 2] (w:1, o:254, a:1, s:1, b:1),
% 11.13/11.54 skol13 [319, 3] (w:1, o:337, a:1, s:1, b:1),
% 11.13/11.54 skol14 [320, 3] (w:1, o:338, a:1, s:1, b:1),
% 11.13/11.54 skol15 [321, 1] (w:1, o:124, a:1, s:1, b:1),
% 11.13/11.54 skol16 [322, 1] (w:1, o:125, a:1, s:1, b:1),
% 11.13/11.54 skol17 [323, 2] (w:1, o:255, a:1, s:1, b:1),
% 11.13/11.54 skol18 [324, 2] (w:1, o:256, a:1, s:1, b:1),
% 11.13/11.54 skol19 [325, 3] (w:1, o:339, a:1, s:1, b:1),
% 11.13/11.54 skol20 [326, 2] (w:1, o:233, a:1, s:1, b:1),
% 11.13/11.54 skol21 [327, 3] (w:1, o:341, a:1, s:1, b:1),
% 11.13/11.54 skol22 [328, 2] (w:1, o:234, a:1, s:1, b:1),
% 11.13/11.54 skol23 [329, 3] (w:1, o:342, a:1, s:1, b:1),
% 11.13/11.54 skol24 [330, 4] (w:1, o:380, a:1, s:1, b:1),
% 11.13/11.54 skol25 [331, 2] (w:1, o:235, a:1, s:1, b:1),
% 11.13/11.54 skol26 [332, 2] (w:1, o:236, a:1, s:1, b:1),
% 11.13/11.54 skol27 [333, 2] (w:1, o:237, a:1, s:1, b:1),
% 11.13/11.54 skol28 [334, 2] (w:1, o:238, a:1, s:1, b:1),
% 11.13/11.54 skol29 [335, 2] (w:1, o:239, a:1, s:1, b:1),
% 11.13/11.54 skol30 [336, 3] (w:1, o:343, a:1, s:1, b:1),
% 11.13/11.54 skol31 [337, 2] (w:1, o:257, a:1, s:1, b:1),
% 11.13/11.54 skol32 [338, 2] (w:1, o:258, a:1, s:1, b:1),
% 11.13/11.54 skol33 [339, 2] (w:1, o:259, a:1, s:1, b:1),
% 11.13/11.54 skol34 [340, 2] (w:1, o:260, a:1, s:1, b:1),
% 11.13/11.54 skol35 [341, 2] (w:1, o:261, a:1, s:1, b:1),
% 11.13/11.54 skol36 [342, 3] (w:1, o:344, a:1, s:1, b:1),
% 11.13/11.54 skol37 [343, 2] (w:1, o:262, a:1, s:1, b:1),
% 11.13/11.54 skol38 [344, 3] (w:1, o:345, a:1, s:1, b:1),
% 11.13/11.54 skol39 [345, 2] (w:1, o:263, a:1, s:1, b:1),
% 11.13/11.54 skol40 [346, 4] (w:1, o:381, a:1, s:1, b:1),
% 11.13/11.54 skol41 [347, 3] (w:1, o:346, a:1, s:1, b:1),
% 11.13/11.54 skol42 [348, 3] (w:1, o:347, a:1, s:1, b:1),
% 11.13/11.54 skol43 [349, 2] (w:1, o:264, a:1, s:1, b:1),
% 11.13/11.54 skol44 [350, 1] (w:1, o:121, a:1, s:1, b:1),
% 11.13/11.54 skol45 [351, 2] (w:1, o:265, a:1, s:1, b:1),
% 11.13/11.54 skol46 [352, 2] (w:1, o:266, a:1, s:1, b:1),
% 11.13/11.54 skol47 [353, 2] (w:1, o:267, a:1, s:1, b:1),
% 11.13/11.54 skol48 [354, 2] (w:1, o:268, a:1, s:1, b:1),
% 11.13/11.54 skol49 [355, 3] (w:1, o:348, a:1, s:1, b:1),
% 11.13/11.54 skol50 [356, 3] (w:1, o:349, a:1, s:1, b:1),
% 11.13/11.54 skol51 [357, 3] (w:1, o:350, a:1, s:1, b:1),
% 11.13/11.54 skol52 [358, 3] (w:1, o:351, a:1, s:1, b:1),
% 11.13/11.54 skol53 [359, 1] (w:1, o:126, a:1, s:1, b:1),
% 11.13/11.54 skol54 [360, 3] (w:1, o:352, a:1, s:1, b:1),
% 11.13/11.54 skol55 [361, 2] (w:1, o:241, a:1, s:1, b:1),
% 11.13/11.54 skol56 [362, 3] (w:1, o:353, a:1, s:1, b:1),
% 11.13/11.54 skol57 [363, 4] (w:1, o:382, a:1, s:1, b:1),
% 11.13/11.54 skol58 [364, 3] (w:1, o:354, a:1, s:1, b:1),
% 11.13/11.54 skol59 [365, 3] (w:1, o:355, a:1, s:1, b:1),
% 11.13/11.54 skol60 [366, 3] (w:1, o:356, a:1, s:1, b:1),
% 11.13/11.54 skol61 [367, 3] (w:1, o:357, a:1, s:1, b:1),
% 11.13/11.54 skol62 [368, 3] (w:1, o:358, a:1, s:1, b:1),
% 11.13/11.54 skol63 [369, 3] (w:1, o:359, a:1, s:1, b:1),
% 11.13/11.54 skol64 [370, 2] (w:1, o:243, a:1, s:1, b:1),
% 11.13/11.54 skol65 [371, 2] (w:1, o:244, a:1, s:1, b:1),
% 11.13/11.54 skol66 [372, 3] (w:1, o:360, a:1, s:1, b:1),
% 11.13/11.54 skol67 [373, 2] (w:1, o:245, a:1, s:1, b:1),
% 11.13/11.54 skol68 [374, 2] (w:1, o:246, a:1, s:1, b:1),
% 11.13/11.54 skol69 [375, 2] (w:1, o:247, a:1, s:1, b:1),
% 11.13/11.54 skol70 [376, 3] (w:1, o:361, a:1, s:1, b:1),
% 11.13/11.54 skol71 [377, 3] (w:1, o:362, a:1, s:1, b:1),
% 11.13/11.54 skol72 [378, 3] (w:1, o:363, a:1, s:1, b:1),
% 11.13/11.54 skol73 [379, 3] (w:1, o:364, a:1, s:1, b:1),
% 11.13/11.54 skol74 [380, 3] (w:1, o:365, a:1, s:1, b:1),
% 11.13/11.54 skol75 [381, 3] (w:1, o:366, a:1, s:1, b:1),
% 11.13/11.54 skol76 [382, 2] (w:1, o:249, a:1, s:1, b:1),
% 11.13/11.54 skol77 [383, 2] (w:1, o:250, a:1, s:1, b:1).
% 11.13/11.54
% 11.13/11.54
% 11.13/11.54 Starting Search:
% 11.13/11.54
% 11.13/11.54 *** allocated 170857 integers for clauses
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 2803
% 66.15/66.51 Kept: 2000
% 66.15/66.51 Inuse: 41
% 66.15/66.51 Deleted: 1
% 66.15/66.51 Deletedinuse: 0
% 66.15/66.51
% 66.15/66.51 *** allocated 256285 integers for clauses
% 66.15/66.51 *** allocated 170857 integers for termspace/termends
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 *** allocated 384427 integers for clauses
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 6255
% 66.15/66.51 Kept: 4240
% 66.15/66.51 Inuse: 211
% 66.15/66.51 Deleted: 5
% 66.15/66.51 Deletedinuse: 0
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 *** allocated 256285 integers for termspace/termends
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 *** allocated 576640 integers for clauses
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 12153
% 66.15/66.51 Kept: 6600
% 66.15/66.51 Inuse: 314
% 66.15/66.51 Deleted: 8
% 66.15/66.51 Deletedinuse: 1
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 18225
% 66.15/66.51 Kept: 8645
% 66.15/66.51 Inuse: 354
% 66.15/66.51 Deleted: 8
% 66.15/66.51 Deletedinuse: 1
% 66.15/66.51
% 66.15/66.51 *** allocated 384427 integers for termspace/termends
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 *** allocated 864960 integers for clauses
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 23880
% 66.15/66.51 Kept: 10735
% 66.15/66.51 Inuse: 393
% 66.15/66.51 Deleted: 10
% 66.15/66.51 Deletedinuse: 2
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 *** allocated 576640 integers for termspace/termends
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 29592
% 66.15/66.51 Kept: 13236
% 66.15/66.51 Inuse: 423
% 66.15/66.51 Deleted: 10
% 66.15/66.51 Deletedinuse: 2
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 39279
% 66.15/66.51 Kept: 15388
% 66.15/66.51 Inuse: 457
% 66.15/66.51 Deleted: 11
% 66.15/66.51 Deletedinuse: 2
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 *** allocated 1297440 integers for clauses
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 51409
% 66.15/66.51 Kept: 17685
% 66.15/66.51 Inuse: 467
% 66.15/66.51 Deleted: 11
% 66.15/66.51 Deletedinuse: 2
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 *** allocated 864960 integers for termspace/termends
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 60896
% 66.15/66.51 Kept: 19711
% 66.15/66.51 Inuse: 507
% 66.15/66.51 Deleted: 11
% 66.15/66.51 Deletedinuse: 2
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 Resimplifying clauses:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 68010
% 66.15/66.51 Kept: 21843
% 66.15/66.51 Inuse: 522
% 66.15/66.51 Deleted: 277
% 66.15/66.51 Deletedinuse: 2
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 77676
% 66.15/66.51 Kept: 24529
% 66.15/66.51 Inuse: 572
% 66.15/66.51 Deleted: 279
% 66.15/66.51 Deletedinuse: 4
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 *** allocated 1946160 integers for clauses
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 90427
% 66.15/66.51 Kept: 27229
% 66.15/66.51 Inuse: 602
% 66.15/66.51 Deleted: 279
% 66.15/66.51 Deletedinuse: 4
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 *** allocated 1297440 integers for termspace/termends
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 101712
% 66.15/66.51 Kept: 29444
% 66.15/66.51 Inuse: 617
% 66.15/66.51 Deleted: 279
% 66.15/66.51 Deletedinuse: 4
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 108301
% 66.15/66.51 Kept: 31455
% 66.15/66.51 Inuse: 661
% 66.15/66.51 Deleted: 280
% 66.15/66.51 Deletedinuse: 5
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 113612
% 66.15/66.51 Kept: 33470
% 66.15/66.51 Inuse: 708
% 66.15/66.51 Deleted: 280
% 66.15/66.51 Deletedinuse: 5
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 119766
% 66.15/66.51 Kept: 35491
% 66.15/66.51 Inuse: 756
% 66.15/66.51 Deleted: 280
% 66.15/66.51 Deletedinuse: 5
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 126860
% 66.15/66.51 Kept: 37548
% 66.15/66.51 Inuse: 782
% 66.15/66.51 Deleted: 280
% 66.15/66.51 Deletedinuse: 5
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 *** allocated 2919240 integers for clauses
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 143072
% 66.15/66.51 Kept: 40582
% 66.15/66.51 Inuse: 817
% 66.15/66.51 Deleted: 280
% 66.15/66.51 Deletedinuse: 5
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 *** allocated 1946160 integers for termspace/termends
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 Resimplifying clauses:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 157247
% 66.15/66.51 Kept: 43798
% 66.15/66.51 Inuse: 837
% 66.15/66.51 Deleted: 687
% 66.15/66.51 Deletedinuse: 5
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 165677
% 66.15/66.51 Kept: 45881
% 66.15/66.51 Inuse: 872
% 66.15/66.51 Deleted: 687
% 66.15/66.51 Deletedinuse: 5
% 66.15/66.51
% 66.15/66.51 Resimplifying inuse:
% 66.15/66.51 Done
% 66.15/66.51
% 66.15/66.51
% 66.15/66.51 Intermediate Status:
% 66.15/66.51 Generated: 170788
% 66.15/66.51 Kept: 48401
% 66.15/66.51 Inuse: 882
% 166.91/167.31 Deleted: 687
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 185357
% 166.91/167.31 Kept: 51645
% 166.91/167.31 Inuse: 917
% 166.91/167.31 Deleted: 687
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 195084
% 166.91/167.31 Kept: 53830
% 166.91/167.31 Inuse: 927
% 166.91/167.31 Deleted: 687
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 205026
% 166.91/167.31 Kept: 56023
% 166.91/167.31 Inuse: 937
% 166.91/167.31 Deleted: 687
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 212440
% 166.91/167.31 Kept: 58486
% 166.91/167.31 Inuse: 957
% 166.91/167.31 Deleted: 687
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 *** allocated 4378860 integers for clauses
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 226075
% 166.91/167.31 Kept: 61500
% 166.91/167.31 Inuse: 986
% 166.91/167.31 Deleted: 687
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying clauses:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 *** allocated 2919240 integers for termspace/termends
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 237241
% 166.91/167.31 Kept: 67867
% 166.91/167.31 Inuse: 1012
% 166.91/167.31 Deleted: 920
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 245642
% 166.91/167.31 Kept: 73267
% 166.91/167.31 Inuse: 1027
% 166.91/167.31 Deleted: 920
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 257534
% 166.91/167.31 Kept: 77913
% 166.91/167.31 Inuse: 1082
% 166.91/167.31 Deleted: 920
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 271093
% 166.91/167.31 Kept: 81208
% 166.91/167.31 Inuse: 1132
% 166.91/167.31 Deleted: 920
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying clauses:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 281847
% 166.91/167.31 Kept: 83379
% 166.91/167.31 Inuse: 1147
% 166.91/167.31 Deleted: 1061
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 289312
% 166.91/167.31 Kept: 85682
% 166.91/167.31 Inuse: 1177
% 166.91/167.31 Deleted: 1061
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 319158
% 166.91/167.31 Kept: 88946
% 166.91/167.31 Inuse: 1187
% 166.91/167.31 Deleted: 1061
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 327075
% 166.91/167.31 Kept: 91008
% 166.91/167.31 Inuse: 1207
% 166.91/167.31 Deleted: 1061
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 *** allocated 6568290 integers for clauses
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 339935
% 166.91/167.31 Kept: 93097
% 166.91/167.31 Inuse: 1252
% 166.91/167.31 Deleted: 1061
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 352019
% 166.91/167.31 Kept: 97644
% 166.91/167.31 Inuse: 1282
% 166.91/167.31 Deleted: 1061
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 *** allocated 4378860 integers for termspace/termends
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 394794
% 166.91/167.31 Kept: 102930
% 166.91/167.31 Inuse: 1307
% 166.91/167.31 Deleted: 1061
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying clauses:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 409491
% 166.91/167.31 Kept: 107912
% 166.91/167.31 Inuse: 1327
% 166.91/167.31 Deleted: 1296
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 417622
% 166.91/167.31 Kept: 110092
% 166.91/167.31 Inuse: 1347
% 166.91/167.31 Deleted: 1296
% 166.91/167.31 Deletedinuse: 5
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 424607
% 166.91/167.31 Kept: 112139
% 166.91/167.31 Inuse: 1372
% 166.91/167.31 Deleted: 1299
% 166.91/167.31 Deletedinuse: 8
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 434340
% 166.91/167.31 Kept: 116468
% 166.91/167.31 Inuse: 1392
% 166.91/167.31 Deleted: 1299
% 166.91/167.31 Deletedinuse: 8
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 440732
% 166.91/167.31 Kept: 119842
% 166.91/167.31 Inuse: 1397
% 166.91/167.31 Deleted: 1300
% 166.91/167.31 Deletedinuse: 9
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 452522
% 166.91/167.31 Kept: 121854
% 166.91/167.31 Inuse: 1443
% 166.91/167.31 Deleted: 1301
% 166.91/167.31 Deletedinuse: 9
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying clauses:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31 Resimplifying inuse:
% 166.91/167.31 Done
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 Intermediate Status:
% 166.91/167.31 Generated: 467134
% 166.91/167.31 Kept: 124076
% 166.91/167.31 Inuse: 1475
% 166.91/167.31 Deleted: 1952
% 166.91/167.31 Deletedinuse: 12
% 166.91/167.31
% 166.91/167.31
% 166.91/167.31 IntermediatCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------