TSTP Solution File: SWW234+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW234+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 23:21:26 EDT 2022
% Result : Timeout 300.02s 300.41s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWW234+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Sun Jun 5 22:00:13 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.99/1.58 *** allocated 10000 integers for termspace/termends
% 0.99/1.58 *** allocated 10000 integers for clauses
% 0.99/1.58 *** allocated 10000 integers for justifications
% 0.99/1.58 *** allocated 15000 integers for termspace/termends
% 0.99/1.58 *** allocated 22500 integers for termspace/termends
% 0.99/1.58 *** allocated 33750 integers for termspace/termends
% 0.99/1.58 Bliksem 1.12
% 0.99/1.58
% 0.99/1.58
% 0.99/1.58 Automatic Strategy Selection
% 0.99/1.58
% 0.99/1.58 *** allocated 50625 integers for termspace/termends
% 0.99/1.58 *** allocated 75937 integers for termspace/termends
% 0.99/1.58 *** allocated 113905 integers for termspace/termends
% 0.99/1.58
% 0.99/1.58 Clauses:
% 0.99/1.58
% 0.99/1.58 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.99/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, v_r____,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_z____ ) ) }.
% 0.99/1.58 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.99/1.58 tc_Complex_Ocomplex ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.99/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.99/1.58 , Y ) }.
% 0.99/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.99/1.58 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.58 v_r____ ) ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.58 v_z____ ) ) }.
% 0.99/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.99/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.99/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.99/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.99/1.58 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.99/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.58 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.99/1.58 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.99/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.58 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.99/1.58 hAPP( Y, U ) ) }.
% 0.99/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.99/1.58 ( Z, skol2( X, Y, Z ) ), hAPP( Y, skol2( X, Y, Z ) ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.58 { ! v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.99/1.58 tc_Complex_Ocomplex ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.58 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.99/1.58 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.58 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.99/1.58 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.99/1.58 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.99/1.58 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.58 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.58 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.99/1.58 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.58 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.58 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.58 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.99/1.58 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.58 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.99/1.58 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.58 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.58 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 T, Y ), Z = Y }.
% 0.99/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 T, Y ) }.
% 0.99/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 Y, Z ), T = Y }.
% 0.99/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 Y, Z ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.58 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.58 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.58 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.58 .
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.58 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.58 .
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.58 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.99/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 Y, Z ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 Z, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.58 ) ) }.
% 0.99/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 T, Y ), Z = Y }.
% 0.99/1.58 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 T, Y ), Z = Y }.
% 0.99/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 Y, T ), Z = Y }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.99/1.58 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.99/1.58 ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.58 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.58 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.58 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.58 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.58 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.99/1.58 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.99/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.99/1.58 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.58 ( X, Y ) ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.58 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.58 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.99/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.58 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.99/1.58 hAPP( Y, U ) ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.58 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.99/1.58 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.99/1.58 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.58 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.58 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.99/1.58 hAPP( Y, U ) ) }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.99/1.58 ( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.99/1.58 ( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.99/1.58 { ! class_Rings_Olinordered__semidom( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.58 c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.99/1.58 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.58 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.58 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.58 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.58 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.58 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.58 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.58 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.99/1.58 ( X, T, Y ) ) ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.58 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.58 tc_RealDef_Oreal ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.58 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.99/1.58 tc_RealDef_Oreal ) }.
% 0.99/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.99/1.58 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.99/1.58 , X ) }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.58 Y ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.58 Y ), ! Z = Y }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.58 Z ), ! Z = Y }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.58 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.58 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.99/1.58 .
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.99/1.58 .
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.58 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.58 .
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.58 .
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.58 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.58 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.58 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.99/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.58 , ! Z = Y }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.58 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.58 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.58 , ! Z = Y }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.58 , ! Y = Z }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.58 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.58 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.99/1.58 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.99/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.99/1.58 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.58 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.58 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.58 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.58 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.99/1.58 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.99/1.58 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.99/1.58 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.58 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.58 X, Y, Z ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.99/1.58 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.99/1.58 .
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.58 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.58 ( X ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.58 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , Z, Y ) }.
% 0.99/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.99/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.99/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.58 tc_RealDef_Oreal ) ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.99/1.58 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.58 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.99/1.58 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.99/1.58 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.99/1.58 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.58 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.58 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.99/1.58 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.99/1.58 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.99/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.58 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.58 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.58 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.58 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.58 , ! Z = Y }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.58 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.58 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.58 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.58 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.99/1.58 ( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.58 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.58 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.58 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.58 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.58 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.58 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.58 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.99/1.58 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.58 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.58 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.58 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.58 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.58 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.58 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.99/1.58 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.58 ( X, Z, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.99/1.58 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.99/1.58 ( X, Z, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.58 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.58 , T ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.58 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.58 , T, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.58 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.58 , Y, T ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.99/1.58 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.58 ( X, Z, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.58 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.58 , T, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.99/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.99/1.58 ( X, T, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.58 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.58 , Y, Z ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.58 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.99/1.58 ( X, Y, Z ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.99/1.58 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.99/1.58 ) }.
% 0.99/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.99/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.99/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.58 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.99/1.58 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.58 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.99/1.58 ) ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.58 ) ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.58 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.58 .
% 0.99/1.58 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.99/1.58 ) }.
% 0.99/1.58 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.99/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.58 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.99/1.58 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.99/1.58 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.99/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.58 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.99/1.58 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.99/1.58 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.58 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.58 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.58 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.58 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.99/1.58 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.58 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.58 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.58 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.99/1.58 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.58 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.99/1.58 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.99/1.58 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.58 , Y, T ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.99/1.58 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.99/1.58 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.99/1.58 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.99/1.58 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.99/1.58 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.99/1.58 Y ) ) ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.99/1.58 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.58 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.58 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.58 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.58 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.58 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.58 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.99/1.58 ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.58 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.99/1.58 ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.58 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.58 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.58 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.58 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.58 ( X, Y ) ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.99/1.58 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.99/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.58 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.99/1.58 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.58 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.58 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.99/1.58 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.99/1.58 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.99/1.58 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.99/1.58 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.58 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.99/1.58 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.99/1.58 ( X, Z, Y ), T ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.99/1.58 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.99/1.58 ( X, Z, Y ) ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.99/1.58 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.99/1.58 { ! c_Polynomial_OpCons( tc_Complex_Ocomplex, v_c____, v_cs____ ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.99/1.58 }.
% 0.99/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.99/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.58 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.99/1.58 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Ozero( X ), !
% 0.99/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.58 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.58 tc_Polynomial_Opoly( X ) ),
% 0.99/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.99/1.58 ), c_Orderings_Oord__class_Oless__eq( X, T, skol3( X, U, W, T ) ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.99/1.58 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.99/1.58 ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.99/1.58 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.99/1.58 hAPP( Z, T ), hAPP( Z, skol3( X, Y, Z, T ) ) ) ),
% 0.99/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.99/1.58 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.99/1.58 ) ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.58 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.99/1.58 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.99/1.58 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.99/1.58 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 0.99/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 0.99/1.58 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.99/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 0.99/1.58 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.99/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 0.99/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 0.99/1.58 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.58 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.99/1.58 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.58 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.99/1.58 ), Y ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.99/1.58 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.99/1.58 }.
% 0.99/1.58 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.58 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.99/1.58 ) }.
% 0.99/1.58 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 0.99/1.58 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.99/1.58 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.58 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.99/1.58 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.58 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.58 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.99/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.58 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.58 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.99/1.58 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.99/1.58 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.99/1.58 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.99/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.58 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.58 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.99/1.58 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.58 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.58 ( X, Y ) ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.99/1.58 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.99/1.58 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.58 ) ), Y ) }.
% 0.99/1.58 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.99/1.58 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.58 ( X, Y ) ) }.
% 0.99/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.99/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.99/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.58 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.58 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 0.99/1.58 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.58 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.99/1.58 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.58 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.58 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.58 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.58 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.58 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.58 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.58 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.58 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.58 c_Complex_Oii ), c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 0.99/1.58 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 0.99/1.58 .
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.99/1.58 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 = Y }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.99/1.58 ( X ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.58 , Y ) }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.58 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.58 = Y }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.58 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.58 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.58 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.58 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.58 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.99/1.58 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.99/1.58 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.99/1.58 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.99/1.58 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.99/1.58 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.99/1.58 ( X, Y ), Z ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.58 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.99/1.58 ( X, Z ), Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.58 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.58 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.99/1.58 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.99/1.58 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.58 Y ) ) = Y }.
% 0.99/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 Z, Y ) ) = Y }.
% 0.99/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.99/1.58 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.99/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.99/1.58 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.99/1.58 .
% 0.99/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.99/1.58 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.99/1.58 }.
% 0.99/1.58 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.58 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.99/1.58 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.58 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.58 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.58 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.58 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.58 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.99/1.58 ), ! U = T }.
% 0.99/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.58 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.99/1.58 ), ! Z = Y }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.99/1.58 ) ), Z ) }.
% 0.99/1.58 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.99/1.58 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.58 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.99/1.58 ) ), T ), Y ) }.
% 0.99/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.58 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.99/1.58 ), U = Z, T = Y }.
% 0.99/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.58 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.58 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.99/1.58 ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.58 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.99/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.99/1.58 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.99/1.58 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.99/1.58 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.99/1.58 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.58 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.58 = Y }.
% 0.99/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.58 = Y }.
% 0.99/1.58 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.58 = Y }.
% 0.99/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.58 = Y }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.58 = Y }.
% 0.99/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.58 = Y }.
% 0.99/1.58 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.99/1.58 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.99/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.99/1.58 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.99/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.99/1.58 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.99/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.99/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.99/1.58 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.99/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.99/1.58 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.99/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.99/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.99/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.58 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.99/1.58 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.99/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.99/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.99/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.99/1.59 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.59 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.99/1.59 }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ), Y ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.59 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.59 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.59 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 , Y ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.59 , Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 X ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.99/1.59 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.99/1.59 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Z ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.99/1.59 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.59 Z ) = Y }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 X, Y ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.99/1.59 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Y ) ) }.
% 0.99/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.59 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.59 X, Z, Y ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.59 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 X, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.99/1.59 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.99/1.59 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.99/1.59 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, Z, Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 0.99/1.59 }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.59 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha1( X, Y
% 0.99/1.59 , Z ), alpha11( X, Y, Z ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha11( X, Y, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ), alpha11( X, Y, Z ) }.
% 0.99/1.59 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.59 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y ), alpha1( X, Y, Z ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) ), alpha2( X, Y, Z ), alpha12( X, Y, Z ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha12( X, Y, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) ) }.
% 0.99/1.59 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ), Y ), alpha12( X, Y, Z ) }.
% 0.99/1.59 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.59 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ), alpha2( X, Y, Z ) }.
% 0.99/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha3( X, Y, Z, T ),
% 0.99/1.59 alpha13( X, Y, Z, T ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha13( X, Y, Z, T ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.59 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha13( X, Y, Z, T ) }.
% 0.99/1.59 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.99/1.59 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.99/1.59 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha3( X, Y, Z, T ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha4( X, Y, Z, T ),
% 0.99/1.59 alpha14( X, Y, Z, T ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha14( X, Y, Z, T ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha14( X, Y, Z, T ) }.
% 0.99/1.59 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.59 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.59 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha4( X, Y, Z, T ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.59 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.59 Z ) ), Y ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.59 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.59 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.99/1.59 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.59 Z ) ), U ), T ) = Y }.
% 0.99/1.59 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.59 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), U ), Y ) }.
% 0.99/1.59 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.59 W ) ), U ), Y ) }.
% 0.99/1.59 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.59 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), U ), Y ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.59 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.59 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.99/1.59 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.99/1.59 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.59 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ) }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.59 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_RealDef_Oreal, Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.99/1.59 , X ) ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.99/1.59 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , c_Groups_Oabs__class_Oabs( X, Y ) ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.59 }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 ), c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 X, Y ) }.
% 0.99/1.59 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.99/1.59 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 0.99/1.59 }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.59 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.99/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.99/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.59 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.59 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.59 X, W, Z ) ), U ), T ), Y ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), U ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.99/1.59 ( X, Z, W ) ), U ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.59 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.99/1.59 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.59 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring__abs( X ), alpha19( X, Z ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.59 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oordered__ring__abs( X ), alpha19( X, Z ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.59 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.59 { ! alpha19( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.59 { ! alpha19( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) ), alpha19( X, Y ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.59 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.59 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.59 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.59 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z )
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) ) ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.99/1.59 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ),
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_RealDef_Oreal, Z, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.99/1.59 , X ) ) ) ) ) }.
% 0.99/1.59 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.99/1.59 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.99/1.59 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.99/1.59 }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, v_r____,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, v_da____,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.99/1.59 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), X ) ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.99/1.59 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.59 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.99/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, v_da____,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.99/1.59 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), v_z____ ) ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, v_da____,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ), hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.99/1.59 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), v_z____ ) ) ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.99/1.59 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.99/1.59 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.99/1.59 ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.99/1.59 }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.99/1.59 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.99/1.59 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.99/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.99/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.99/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.99/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.99/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.99/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.99/1.59 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.99/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.99/1.59 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.99/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.99/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.99/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y ) }.
% 0.99/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y ) = Y }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.99/1.59 ( X ) ) ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.99/1.59 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.99/1.59 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.99/1.59 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.99/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.99/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.99/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.99/1.59 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.99/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.99/1.59 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.99/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.99/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.99/1.59 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.99/1.59 tc_Complex_Ocomplex ) ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.59 tc_RealDef_Oreal, skol4( X, Y ), c_RealVector_Onorm__class_Onorm(
% 0.99/1.59 tc_Complex_Ocomplex, Z ) ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.59 tc_RealDef_Oreal, Y, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.99/1.59 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.99/1.59 tc_Complex_Ocomplex, X, v_cs____ ) ), Z ) ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, skol5,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, v_da____,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.99/1.59 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), X ) ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.99/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.99/1.59 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol6( X, Y ) ) }.
% 0.99/1.59 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.99/1.59 ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.99/1.59 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.99/1.59 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.99/1.59 ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.99/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.99/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.99/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.99/1.59 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.59 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.59 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.59 tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.99/1.59 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.99/1.59 .
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.99/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.99/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.99/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.59 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.59 , alpha5( X, Y, Z ) }.
% 0.99/1.59 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.59 , alpha15( X, Y, Z ) }.
% 0.99/1.59 { ! alpha5( X, Y, Z ), ! alpha15( X, Y, Z ), hBOOL( hAPP( Z,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.59 { ! alpha15( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.99/1.59 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.99/1.59 { ! hBOOL( hAPP( Z, skol7( T, U, Z ) ) ), alpha15( X, Y, Z ) }.
% 0.99/1.59 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol7( X, Y, Z ) ),
% 0.99/1.59 alpha15( X, Y, Z ) }.
% 0.99/1.59 { ! alpha5( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.99/1.59 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha5( X, Y, Z ) }.
% 0.99/1.59 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha5
% 0.99/1.59 ( X, Y, Z ) }.
% 0.99/1.59 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.59 , ! alpha6( X, Y, Z ) }.
% 0.99/1.59 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.59 , ! alpha16( X, Y, Z ) }.
% 0.99/1.59 { alpha6( X, Y, Z ), alpha16( X, Y, Z ), hBOOL( hAPP( Z,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.59 { ! alpha16( X, Y, Z ), ! hBOOL( hAPP( Z, skol8( T, U, Z ) ) ) }.
% 0.99/1.59 { ! alpha16( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.99/1.59 skol8( X, Y, Z ) ) }.
% 0.99/1.59 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.99/1.59 ) ), alpha16( X, Y, Z ) }.
% 0.99/1.59 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.99/1.59 .
% 0.99/1.59 { ! alpha6( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ) ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6( X, Y, Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.99/1.59 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.99/1.59 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.99/1.59 { alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.99/1.59 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.99/1.59 { alpha20( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.99/1.59 ( X, Y ), Z ) ) }.
% 0.99/1.59 { ! alpha20( X, Y, Z ), alpha21( X, Y, Z ), Z = Y }.
% 0.99/1.59 { ! alpha20( X, Y, Z ), alpha21( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.99/1.59 ) ) }.
% 0.99/1.59 { ! alpha21( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.99/1.59 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha20( X, Y, Z ) }.
% 0.99/1.59 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.99/1.59 }.
% 0.99/1.59 { ! alpha21( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.99/1.59 X, Y ), Z ) ), alpha21( X, Y, Z ) }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.99/1.59 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.99/1.59 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.99/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.59 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.99/1.59 .
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), X ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), X ) = X }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ) ) = X }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.99/1.59 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.99/1.59 .
% 0.99/1.59 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.99/1.59 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.99/1.59 .
% 0.99/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.99/1.59 , X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.99/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol9( X, Y ) ) }.
% 0.99/1.59 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.59 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.99/1.59 ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.59 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.99/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.99/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.59 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.59 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.99/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.59 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.99/1.59 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Nat_Onat ) }.
% 0.99/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Nat_Onat ) }.
% 0.99/1.59 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.99/1.59 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.59 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.59 , Y ), X ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.59 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.59 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 Y ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.59 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, X ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.99/1.59 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.59 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.99/1.59 ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.59 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.59 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.99/1.59 ) }.
% 0.99/1.59 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.99/1.59 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.59 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.59 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, X ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.99/1.59 ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.99/1.59 ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.99/1.59 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.99/1.59 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.99/1.59 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.99/1.59 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10( Z, T ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol10( X, Y ) ) ) }.
% 0.99/1.59 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.99/1.59 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.99/1.59 ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.99/1.59 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.99/1.59 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.99/1.59 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.99/1.59 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.59 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.59 }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.99/1.59 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.99/1.59 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol11( Y ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol11( X ) ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol12( Z, T ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol12( X, Y ) ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.59 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.99/1.59 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.99/1.59 }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.99/1.59 ), c_RComplete_Onatfloor( X ) ) }.
% 0.99/1.59 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.99/1.59 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.99/1.59 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.99/1.59 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol13( T, U, W ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ), skol13( X,
% 0.99/1.59 Y, Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP(
% 0.99/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), T ), hAPP(
% 0.99/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), Z ) ) ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.59 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.59 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Nat_Onat ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.59 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha7
% 0.99/1.59 ( X, Y, Z ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.59 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! alpha7( X, Y, Z ),
% 0.99/1.59 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.99/1.59 { ! alpha7( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.99/1.59 ( X ) ) }.
% 0.99/1.59 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.59 alpha7( X, Y, Z ) }.
% 0.99/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, X ) ) }.
% 0.99/1.59 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.99/1.59 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.99/1.59 Y = X }.
% 0.99/1.59 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.99/1.59 , X ) }.
% 0.99/1.59 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 0.99/1.59 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 0.99/1.59 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.99/1.59 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.59 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.59 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.99/1.59 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.59 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.59 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.99/1.59 ( tc_Nat_Onat, X ) ) }.
% 0.99/1.59 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.99/1.59 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.99/1.59 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.99/1.59 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.99/1.59 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.59 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.59 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.59 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 0.99/1.59 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.59 , c_RComplete_Onatfloor( X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.99/1.59 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_RComplete_Onatceiling( Y ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.59 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.59 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.59 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_RealDef_Oreal ) ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.59 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.59 , X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.99/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.59 , c_RComplete_Onatfloor( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.59 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.99/1.59 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.59 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_RComplete_Onatceiling( X ), Y ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_RealDef_Oreal ) ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.59 c_RComplete_Onatfloor( X ), Y ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.59 c_RComplete_Onatceiling( X ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_RComplete_Onatfloor( X ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.99/1.59 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.99/1.59 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.99/1.59 c_RComplete_Onatfloor( X ) = Y }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.99/1.59 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol14( X ),
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, skol14( X ) ) ) }.
% 0.99/1.59 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.99/1.59 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.59 tc_Nat_Onat, skol15( X, Y ), skol30( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.99/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 hAPP( Y, skol30( X, Y ) ), hAPP( Y, skol15( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.99/1.59 , Y ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol16( Z, T ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol16( X, Y ) ) }.
% 0.99/1.59 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.59 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.59 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol17( T, U, W ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol17( X, Y,
% 0.99/1.59 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, T ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol17( X, Y,
% 0.99/1.59 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, T, Z ) }.
% 0.99/1.59 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.99/1.59 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.99/1.59 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.99/1.59 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.99/1.59 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.99/1.59 hAPP( Z, Y ) ) }.
% 0.99/1.59 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.99/1.59 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.99/1.59 ) ) }.
% 0.99/1.59 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ), Z = Y }.
% 0.99/1.59 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.99/1.59 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.99/1.59 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.99/1.59 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.59 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol18( Z, Y
% 0.99/1.59 ), Y ) }.
% 0.99/1.59 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.59 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.59 skol18( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.99/1.59 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.59 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.99/1.59 , skol18( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol19( Y ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol19( X ) ) ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.99/1.59 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.99/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.99/1.59 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.99/1.59 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol20( Z, T ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol20( X, Y ) ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol21( Z, T ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol21( X, Y ) ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.59 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.99/1.59 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, Y ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.99/1.59 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.99/1.59 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.99/1.59 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Nat_Onat ) ) = Y }.
% 0.99/1.59 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.59 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.99/1.59 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.99/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.99/1.59 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.99/1.59 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.59 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.99/1.59 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.59 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.99/1.59 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.59 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.99/1.59 ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.99/1.59 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.99/1.59 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.99/1.59 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.99/1.59 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.59 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.59 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.59 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.59 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.99/1.59 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.59 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.99/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.59 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.99/1.59 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.59 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.99/1.59 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.99/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.59 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.99/1.59 ( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) }.
% 0.99/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.59 = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.99/1.59 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Nat_Onat ) ) = Y }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.99/1.59 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.59 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.59 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ) }.
% 0.99/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.59 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.99/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.99/1.59 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.59 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.99/1.59 ( hAPP( c_Power_Opower__class_Opower( X ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) =
% 0.99/1.59 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.59 ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.99/1.59 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.59 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.59 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.99/1.59 ) ) }.
% 0.99/1.59 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.59 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.99/1.59 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.99/1.59 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.99/1.59 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.99/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.99/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol22( X, Y ) ), Y
% 0.99/1.59 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.59 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.99/1.59 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.59 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Y ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.99/1.59 ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.99/1.59 tc_Int_Oint, Y ) ), X ) ) }.
% 0.99/1.59 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.99/1.59 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.99/1.59 tc_Int_Oint, X ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.99/1.59 tc_Int_Oint, X ) = X }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.59 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Int_Oint ) }.
% 0.99/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Int_Oint ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.99/1.59 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.99/1.59 .
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.99/1.59 ( tc_Int_Oint ) ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Int_Oint ) ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.99/1.59 }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Int_Oint ) ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.99/1.59 }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Int_Oint ) ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Int_Oint ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.99/1.59 = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Int_Oint ) ) ) }.
% 0.99/1.59 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Int_Oint ) ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.99/1.59 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.99/1.59 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.59 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.59 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.99/1.59 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.59 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.99/1.59 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Int_Oint ) ) = X }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Int_Oint ), X ) = X }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.99/1.59 ( tc_Int_Oint ) }.
% 0.99/1.59 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.99/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.99/1.59 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.99/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.99/1.59 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.99/1.59 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.99/1.59 ( tc_Int_Oint ), Y ) }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.59 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.99/1.59 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.99/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.60 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.99/1.60 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.99/1.60 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.60 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.60 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, X, Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Int_Oint, X, Y ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.99/1.60 ) }.
% 0.99/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.99/1.60 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.60 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.99/1.60 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Orcis( Y
% 0.99/1.60 , X ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 0.99/1.60 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.99/1.60 ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.60 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Int_Oint, X, Y ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.99/1.60 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.99/1.60 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.99/1.60 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol23( Z, Y ) ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.99/1.60 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.99/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Int_Oint, skol23( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.60 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.99/1.60 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.99/1.60 , Z ), X ) ) ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.99/1.60 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.99/1.60 hAPP( Z, skol24( U, W, Z ) ) ) }.
% 0.99/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.99/1.60 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol24( X
% 0.99/1.60 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.99/1.60 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol31( X,
% 0.99/1.60 Y, Z ) ) ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 c_Groups_Oabs__class_Oabs( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.60 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oabs__class_Oabs( X, Y ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.60 ), c_Rings_Odvd__class_Odvd( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oabs__class_Oabs( X, Z )
% 0.99/1.60 = c_Groups_Oabs__class_Oabs( X, Y ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 Z, T ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.99/1.60 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.99/1.60 , Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.99/1.60 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.99/1.60 , Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.99/1.60 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.60 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.60 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.60 ), T ), U ), Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.99/1.60 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.99/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.99/1.60 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.99/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.99/1.60 ( X ), Y ), Z ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.99/1.60 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.99/1.60 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.99/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.99/1.60 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.99/1.60 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.99/1.60 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.99/1.60 Y ) ) ), Y ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.99/1.60 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.99/1.60 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.99/1.60 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.99/1.60 Y ) ) ), Y ) }.
% 0.99/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.99/1.60 X ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.99/1.60 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.60 X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.99/1.60 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), c_Groups_Oabs__class_Oabs
% 0.99/1.60 ( tc_Int_Oint, Y ) = c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Int_Oint, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.99/1.60 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.99/1.60 .
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.99/1.60 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 0.99/1.60 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 0.99/1.60 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.60 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) =
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.60 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) = c_Groups_Oone__class_Oone
% 0.99/1.60 ( tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, X,
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.99/1.60 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.99/1.60 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.99/1.60 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.99/1.60 ) ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.99/1.60 , Z ), X ) ), T ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, U, T ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol25( X, Y ) ) ) }.
% 0.99/1.60 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.99/1.60 .
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.99/1.60 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.99/1.60 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.60 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.60 ), X ) ) }.
% 0.99/1.60 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha8( X, Y ), alpha17
% 0.99/1.60 ( X, Y ) }.
% 0.99/1.60 { ! alpha8( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.60 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! alpha17( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.60 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! alpha17( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! alpha17( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha17( X, Y ) }.
% 0.99/1.60 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.99/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha9( X, Y ), alpha18( X
% 0.99/1.60 , Y ) }.
% 0.99/1.60 { ! alpha9( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! alpha18( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! alpha18( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! alpha18( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha18( X, Y ) }.
% 0.99/1.60 { ! alpha9( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! alpha9( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 0.99/1.60 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.99/1.60 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.99/1.60 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.99/1.60 }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.99/1.60 c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.60 , c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.99/1.60 .
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.99/1.60 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.99/1.60 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.99/1.60 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.99/1.60 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.99/1.60 { ! c_Nat_OSuc( X ) = X }.
% 0.99/1.60 { ! X = c_Nat_OSuc( X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.99/1.60 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.99/1.60 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.99/1.60 .
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.99/1.60 .
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.99/1.60 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.99/1.60 X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.99/1.60 }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.60 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.60 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.99/1.60 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.99/1.60 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.60 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol26( X ) ) }.
% 0.99/1.60 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 0.99/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.60 c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! alpha10( X, Y ), Y = c_Nat_OSuc( skol27( Z, Y ) ) }.
% 0.99/1.60 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol27( X
% 0.99/1.60 , Y ), X ) }.
% 0.99/1.60 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.99/1.60 ), alpha10( X, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.60 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.60 ), X ) ) }.
% 0.99/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.99/1.60 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.99/1.60 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.99/1.60 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.99/1.60 ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.60 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.60 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.99/1.60 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.99/1.60 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.99/1.60 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.60 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), Y ), Z = Y }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.99/1.60 ( tc_Int_Oint, Y ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.60 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.60 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.99/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.99/1.60 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.99/1.60 ) ) = X }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.60 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.99/1.60 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.60 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.60 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.99/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.99/1.60 c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ),
% 0.99/1.60 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.60 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ) }.
% 0.99/1.60 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.60 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.99/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.99/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.99/1.60 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.99/1.60 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.60 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol28( X, Y, Z ) ) ), Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.99/1.60 tc_Nat_Onat, c_Nat_OSuc( skol32( X, Y ) ) ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol34( X, Y, Z ) ) ),
% 0.99/1.60 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol36( T, U ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol34( X, Y, Z ) ) ),
% 0.99/1.60 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol36( X, Y ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol29( X, Y, Z ) ) ), Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.99/1.60 tc_Nat_Onat, c_Nat_OSuc( skol33( X, Y ) ) ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol35( X, Y, Z ) ) ),
% 0.99/1.60 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol37( T, U ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol35( X, Y, Z ) ) ),
% 0.99/1.60 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol37( X, Y ) ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.99/1.60 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.99/1.60 ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Nat_Onat, Z, X ) }.
% 0.99/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.99/1.60 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.60 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.60 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.99/1.60 ( tc_fun( Y, X ) ) }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.99/1.60 ) ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.99/1.60 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.99/1.60 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.99/1.60 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.60 tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.99/1.60 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.99/1.60 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.99/1.60 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.99/1.60 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.99/1.60 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.99/1.60 { class_Power_Opower( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.99/1.60 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.99/1.60 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.99/1.60 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.60 tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.99/1.60 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.99/1.60 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.99/1.60 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.99/1.60 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.99/1.60 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.99/1.60 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.99/1.60 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.60 tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.99/1.60 .
% 0.99/1.60 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Oabs__if( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 0.99/1.60 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.60 tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ),
% 0.99/1.60 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.99/1.60 ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.99/1.60 X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.60 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.60 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.60 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.99/1.60 ( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.99/1.60 ( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), class_Groups_Oabs__if(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.99/1.60 ) ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.99/1.60 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.99/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_z____ ) ) }.
% 0.99/1.60
% 0.99/1.60 *** allocated 15000 integers for clauses
% 0.99/1.60 *** allocated 22500 integers for clauses
% 0.99/1.60 *** allocated 33750 integers for clauses
% 0.99/1.60 *** allocated 50625 integers for clauses
% 0.99/1.60 *** allocated 75937 integers for clauses
% 0.99/1.60 percentage equality = 0.251323, percentage horn = 0.925325
% 0.99/1.60 This is a problem with some equality
% 0.99/1.60
% 0.99/1.60
% 0.99/1.60
% 0.99/1.60 Options Used:
% 0.99/1.60
% 0.99/1.60 useres = 1
% 0.99/1.60 useparamod = 1
% 0.99/1.60 useeqrefl = 1
% 0.99/1.60 useeqfact = 1
% 0.99/1.60 usefactor = 1
% 0.99/1.60 usesimpsplitting = 0
% 0.99/1.60 usesimpdemod = 5
% 0.99/1.60 usesimpres = 3
% 0.99/1.60
% 0.99/1.60 resimpinuse = 1000
% 0.99/1.60 resimpclauses = 20000
% 0.99/1.60 substype = eqrewr
% 0.99/1.60 backwardsubs = 1
% 0.99/1.60 selectoldest = 5
% 0.99/1.60
% 0.99/1.60 litorderings [0] = split
% 0.99/1.60 litorderings [1] = extend the termordering, first sorting on arguments
% 0.99/1.60
% 0.99/1.60 termordering = kbo
% 0.99/1.60
% 0.99/1.60 litapriori = 0
% 0.99/1.60 termapriori = 1
% 0.99/1.60 litaposteriori = 0
% 0.99/1.60 termaposteriori = 0
% 0.99/1.60 demodaposteriori = 0
% 0.99/1.60 ordereqreflfact = 0
% 0.99/1.60
% 0.99/1.60 litselect = negord
% 0.99/1.60
% 0.99/1.60 maxweight = 15
% 0.99/1.60 maxdepth = 30000
% 0.99/1.60 maxlength = 115
% 0.99/1.60 maxnrvars = 195
% 0.99/1.60 excuselevel = 1
% 0.99/1.60 increasemaxweight = 1
% 0.99/1.60
% 0.99/1.60 maxselected = 10000000
% 0.99/1.60 maxnrclauses = 10000000
% 0.99/1.60
% 0.99/1.60 showgenerated = 0
% 0.99/1.60 showkept = 0
% 0.99/1.60 showselected = 0
% 0.99/1.60 showdeleted = 0
% 0.99/1.60 showresimp = 1
% 0.99/1.60 showstatus = 2000
% 0.99/1.60
% 0.99/1.60 prologoutput = 0
% 0.99/1.60 nrgoals = 5000000
% 0.99/1.60 totalproof = 1
% 0.99/1.60
% 0.99/1.60 Symbols occurring in the translation:
% 0.99/1.60
% 0.99/1.60 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.99/1.60 . [1, 2] (w:1, o:198, a:1, s:1, b:0),
% 0.99/1.60 ! [4, 1] (w:0, o:113, a:1, s:1, b:0),
% 0.99/1.60 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.99/1.60 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.99/1.60 hAPP [38, 2] (w:1, o:222, a:1, s:1, b:0),
% 0.99/1.60 tc_RealDef_Oreal [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.99/1.60 v_r____ [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.99/1.60 tc_Complex_Ocomplex [41, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.99/1.60 v_z____ [42, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.99/1.60 c_RealVector_Onorm__class_Onorm [43, 2] (w:1, o:223, a:1, s:1, b:0),
% 0.99/1.60
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq [44, 3] (w:1, o:262, a:1, s:1, b:0)
% 0.99/1.60 ,
% 0.99/1.60 v_p [45, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.99/1.60 tc_Polynomial_Opoly [46, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.99/1.60 c_Groups_Ozero__class_Ozero [47, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.99/1.60 class_RealVector_Oreal__normed__algebra__1 [49, 1] (w:1, o:124, a:1
% 0.99/1.60 , s:1, b:0),
% 0.99/1.60 c_Groups_Oone__class_Oone [50, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.99/1.60 class_Orderings_Opreorder [52, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.99/1.60 c_Groups_Oabs__class_Oabs [53, 2] (w:1, o:225, a:1, s:1, b:0),
% 0.99/1.60 c_Groups_Oplus__class_Oplus [54, 3] (w:1, o:263, a:1, s:1, b:0),
% 0.99/1.60 class_Groups_Oone [61, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.99/1.60 class_Orderings_Oord [63, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.99/1.60 tc_fun [64, 2] (w:1, o:246, a:1, s:1, b:0),
% 0.99/1.60 class_Orderings_Olinorder [66, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.99/1.60 v_cs____ [67, 0] (w:1, o:40, a:1, s:1, b:0),
% 0.99/1.60 class_Groups_Oordered__ab__group__add__abs [69, 1] (w:1, o:131, a:1
% 0.99/1.60 , s:1, b:0),
% 0.99/1.60 class_RealVector_Oreal__normed__vector [70, 1] (w:1, o:132, a:1, s:1
% 0.99/1.60 , b:0),
% 0.99/1.60 class_Groups_Omonoid__add [73, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.99/1.60 class_Groups_Ocomm__monoid__add [74, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.99/1.60
% 0.99/1.60 class_Groups_Ozero [75, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.99/1.60 class_Groups_Olinordered__ab__group__add [77, 1] (w:1, o:133, a:1, s:
% 0.99/1.60 1, b:0),
% 0.99/1.60 class_Groups_Oab__semigroup__add [79, 1] (w:1, o:137, a:1, s:1, b:0)
% 0.99/1.60 ,
% 0.99/1.60 class_Groups_Ocancel__semigroup__add [82, 1] (w:1, o:138, a:1, s:1
% 0.99/1.60 , b:0),
% 0.99/1.60 class_Groups_Oordered__comm__monoid__add [83, 1] (w:1, o:139, a:1, s:
% 0.99/1.60 1, b:0),
% 0.99/1.60 class_Groups_Ocancel__ab__semigroup__add [85, 1] (w:1, o:140, a:1, s:
% 0.99/1.60 1, b:0),
% 0.99/1.60 class_Groups_Oordered__ab__semigroup__add__imp__le [86, 1] (w:1, o:
% 0.99/1.60 141, a:1, s:1, b:0),
% 0.99/1.60 class_Groups_Oordered__ab__semigroup__add [88, 1] (w:1, o:142, a:1
% 0.99/1.60 , s:1, b:0),
% 0.99/1.60 class_Orderings_Oorder [89, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Olinordered__semidom [90, 1] (w:1, o:145, a:1, s:1, b:0)
% 0.99/1.60 ,
% 0.99/1.60 class_Rings_Olinordered__idom [91, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Ozero__neq__one [92, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Ocomm__semiring__1 [93, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.99/1.60 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [94
% 0.99/1.60 , 1] (w:1, o:175, a:1, s:1, b:0),
% 0.99/1.60 c_Groups_Ominus__class_Ominus [95, 3] (w:1, o:264, a:1, s:1, b:0),
% 0.99/1.60 c_Groups_Osgn__class_Osgn [96, 2] (w:1, o:247, a:1, s:1, b:0),
% 0.99/1.60 c_Orderings_Oord__class_Oless [97, 3] (w:1, o:265, a:1, s:1, b:0),
% 0.99/1.60 class_Groups_Oab__group__add [99, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.99/1.60 class_Groups_Oordered__ab__group__add [100, 1] (w:1, o:177, a:1, s:1
% 0.99/1.60 , b:0),
% 0.99/1.60 class_Groups_Ogroup__add [101, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.99/1.60 class_Groups_Oordered__cancel__ab__semigroup__add [102, 1] (w:1, o:
% 0.99/1.60 179, a:1, s:1, b:0),
% 0.99/1.60 class_Groups_Osgn__if [103, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.99/1.60 v_c____ [106, 0] (w:1, o:62, a:1, s:1, b:0),
% 0.99/1.60 c_Polynomial_OpCons [107, 3] (w:1, o:267, a:1, s:1, b:0),
% 0.99/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [109, 2] (w:1, o:
% 0.99/1.60 224, a:1, s:1, b:0),
% 0.99/1.60 tc_Nat_Onat [110, 0] (w:1, o:69, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Olinordered__semiring__1__strict [116, 1] (w:1, o:152, a:
% 0.99/1.60 1, s:1, b:0),
% 0.99/1.60 c_Groups_Otimes__class_Otimes [117, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.99/1.60 c_Complex_Oii [118, 0] (w:1, o:75, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Olinordered__semiring__1 [119, 1] (w:1, o:153, a:1, s:1
% 0.99/1.60 , b:0),
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus [120, 2] (w:1, o:248, a:1, s:1, b:0)
% 0.99/1.60 ,
% 0.99/1.60 class_Rings_Ocomm__ring__1 [121, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Oring__1__no__zero__divisors [122, 1] (w:1, o:154, a:1
% 0.99/1.60 , s:1, b:0),
% 0.99/1.60 class_Rings_Oidom [123, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Oring [128, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.99/1.60 class_RealVector_Oreal__normed__div__algebra [129, 1] (w:1, o:157, a:
% 0.99/1.60 1, s:1, b:0),
% 0.99/1.60 class_Groups_Oab__semigroup__mult [130, 1] (w:1, o:182, a:1, s:1, b:0
% 0.99/1.60 ),
% 0.99/1.60 class_RealVector_Oreal__normed__algebra [131, 1] (w:1, o:158, a:1, s:
% 0.99/1.60 1, b:0),
% 0.99/1.60 class_Rings_Omult__zero [133, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Oring__no__zero__divisors [134, 1] (w:1, o:163, a:1, s:1
% 0.99/1.60 , b:0),
% 0.99/1.60 class_Rings_Ono__zero__divisors [135, 1] (w:1, o:164, a:1, s:1, b:0)
% 0.99/1.60 ,
% 0.99/1.60 class_Rings_Ocomm__semiring [139, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Osemiring [142, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.99/1.60 class_Groups_Ocomm__monoid__mult [145, 1] (w:1, o:183, a:1, s:1, b:0)
% 0.99/1.60 ,
% 0.99/1.60 class_Groups_Omonoid__mult [146, 1] (w:1, o:184, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Olinordered__ring [149, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Olinordered__ring__strict [150, 1] (w:1, o:144, a:1, s:1
% 0.99/1.60 , b:0),
% 0.99/1.60 class_Rings_Oordered__cancel__semiring [151, 1] (w:1, o:168, a:1, s:1
% 0.99/1.60 , b:0),
% 0.99/1.60 class_Rings_Oordered__ring [152, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Oordered__semiring [153, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.99/1.60
% 0.99/1.60 class_Rings_Oordered__comm__semiring [154, 1] (w:1, o:172, a:1, s:1
% 0.99/1.60 , b:0),
% 0.99/1.60 class_Rings_Olinordered__comm__semiring__strict [155, 1] (w:1, o:159
% 0.99/1.60 , a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Olinordered__semiring__strict [156, 1] (w:1, o:160, a:1
% 0.99/1.60 , s:1, b:0),
% 0.99/1.60 class_Groups_Oabs__if [159, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Olinordered__semiring [160, 1] (w:1, o:161, a:1, s:1, b:0
% 0.99/1.60 ),
% 0.99/1.60 class_Rings_Oring__1 [161, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Oordered__ring__abs [162, 1] (w:1, o:170, a:1, s:1, b:0)
% 0.99/1.60 ,
% 0.99/1.60 v_da____ [165, 0] (w:1, o:89, a:1, s:1, b:0),
% 0.99/1.60 v_aa____ [166, 0] (w:1, o:90, a:1, s:1, b:0),
% 0.99/1.60 c_Polynomial_Opoly [167, 2] (w:1, o:249, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Ocomm__ring [169, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.99/1.60 class_Rings_Ocomm__semiring__0 [171, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.99/1.60
% 0.99/1.60 class_Int_Oring__char__0 [173, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.99/1.60 c_Polynomial_Osynthetic__div [176, 3] (w:1, o:268, a:1, s:1, b:0),
% 0.99/1.60 hBOOL [185, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.99/1.60 c_Polynomial_Opcompose [189, 3] (w:1, o:269, a:1, s:1, b:0),
% 0.99/1.60 c_Polynomial_Oorder [190, 3] (w:1, o:266, a:1, s:1, b:0),
% 4.21/4.56 c_RComplete_Onatceiling [191, 1] (w:1, o:188, a:1, s:1, b:0),
% 4.21/4.56 c_RComplete_Onatfloor [195, 1] (w:1, o:189, a:1, s:1, b:0),
% 4.21/4.56 c_RealDef_Oreal [197, 2] (w:1, o:250, a:1, s:1, b:0),
% 4.21/4.56 c_Polynomial_Opos__poly [198, 2] (w:1, o:251, a:1, s:1, b:0),
% 4.21/4.56 c_SEQ_Odecseq [199, 2] (w:1, o:252, a:1, s:1, b:0),
% 4.21/4.56 class_Lattices_Oboolean__algebra [201, 1] (w:1, o:191, a:1, s:1, b:0)
% 4.21/4.56 ,
% 4.21/4.56 class_Lattices_Oab__semigroup__idem__mult [203, 1] (w:1, o:190, a:1
% 4.21/4.56 , s:1, b:0),
% 4.21/4.56 class_Groups_Ominus [206, 1] (w:1, o:192, a:1, s:1, b:0),
% 4.21/4.56 class_Groups_Ouminus [207, 1] (w:1, o:193, a:1, s:1, b:0),
% 4.21/4.56 c_Polynomial_Opoly__rec [208, 5] (w:1, o:300, a:1, s:1, b:0),
% 4.21/4.56 c_fequal [210, 2] (w:1, o:253, a:1, s:1, b:0),
% 4.21/4.56 c_If [211, 4] (w:1, o:294, a:1, s:1, b:0),
% 4.21/4.56 c_Power_Opower__class_Opower [212, 1] (w:1, o:194, a:1, s:1, b:0),
% 4.21/4.56 class_Power_Opower [213, 1] (w:1, o:195, a:1, s:1, b:0),
% 4.21/4.56 tc_Int_Oint [214, 0] (w:1, o:106, a:1, s:1, b:0),
% 4.21/4.56 class_Rings_Osemiring__0 [215, 1] (w:1, o:173, a:1, s:1, b:0),
% 4.21/4.56 c_Power_Opower_Opower [217, 3] (w:1, o:270, a:1, s:1, b:0),
% 4.21/4.56 c_Nat__Transfer_Otsub [224, 2] (w:1, o:254, a:1, s:1, b:0),
% 4.21/4.56 c_Complex_Orcis [225, 2] (w:1, o:255, a:1, s:1, b:0),
% 4.21/4.56 c_Rings_Odvd__class_Odvd [228, 3] (w:1, o:271, a:1, s:1, b:0),
% 4.21/4.56 class_Rings_Odvd [229, 1] (w:1, o:174, a:1, s:1, b:0),
% 4.21/4.56 c_Nat_OSuc [232, 1] (w:1, o:196, a:1, s:1, b:0),
% 4.21/4.56 class_Groups_Ocancel__comm__monoid__add [240, 1] (w:1, o:197, a:1, s:
% 4.21/4.56 1, b:0),
% 4.21/4.56 tc_HOL_Obool [242, 0] (w:1, o:105, a:1, s:1, b:0),
% 4.21/4.56 alpha1 [243, 3] (w:1, o:272, a:1, s:1, b:1),
% 4.21/4.56 alpha2 [244, 3] (w:1, o:277, a:1, s:1, b:1),
% 4.21/4.56 alpha3 [245, 4] (w:1, o:295, a:1, s:1, b:1),
% 4.21/4.56 alpha4 [246, 4] (w:1, o:296, a:1, s:1, b:1),
% 4.21/4.56 alpha5 [247, 3] (w:1, o:278, a:1, s:1, b:1),
% 4.21/4.56 alpha6 [248, 3] (w:1, o:279, a:1, s:1, b:1),
% 4.21/4.56 alpha7 [249, 3] (w:1, o:280, a:1, s:1, b:1),
% 4.21/4.56 alpha8 [250, 2] (w:1, o:256, a:1, s:1, b:1),
% 4.21/4.56 alpha9 [251, 2] (w:1, o:257, a:1, s:1, b:1),
% 4.21/4.56 alpha10 [252, 2] (w:1, o:258, a:1, s:1, b:1),
% 4.21/4.56 alpha11 [253, 3] (w:1, o:273, a:1, s:1, b:1),
% 4.21/4.56 alpha12 [254, 3] (w:1, o:274, a:1, s:1, b:1),
% 4.21/4.56 alpha13 [255, 4] (w:1, o:297, a:1, s:1, b:1),
% 4.21/4.56 alpha14 [256, 4] (w:1, o:298, a:1, s:1, b:1),
% 4.21/4.56 alpha15 [257, 3] (w:1, o:275, a:1, s:1, b:1),
% 4.21/4.56 alpha16 [258, 3] (w:1, o:276, a:1, s:1, b:1),
% 4.21/4.56 alpha17 [259, 2] (w:1, o:259, a:1, s:1, b:1),
% 4.21/4.56 alpha18 [260, 2] (w:1, o:260, a:1, s:1, b:1),
% 4.21/4.56 alpha19 [261, 2] (w:1, o:261, a:1, s:1, b:1),
% 4.21/4.56 alpha20 [262, 3] (w:1, o:281, a:1, s:1, b:1),
% 4.21/4.56 alpha21 [263, 3] (w:1, o:282, a:1, s:1, b:1),
% 4.21/4.56 skol1 [264, 2] (w:1, o:226, a:1, s:1, b:1),
% 4.21/4.56 skol2 [265, 3] (w:1, o:285, a:1, s:1, b:1),
% 4.21/4.56 skol3 [266, 4] (w:1, o:299, a:1, s:1, b:1),
% 4.21/4.56 skol4 [267, 2] (w:1, o:232, a:1, s:1, b:1),
% 4.21/4.56 skol5 [268, 0] (w:1, o:12, a:1, s:1, b:1),
% 4.21/4.56 skol6 [269, 2] (w:1, o:233, a:1, s:1, b:1),
% 4.21/4.56 skol7 [270, 3] (w:1, o:286, a:1, s:1, b:1),
% 4.21/4.56 skol8 [271, 3] (w:1, o:287, a:1, s:1, b:1),
% 4.21/4.56 skol9 [272, 2] (w:1, o:234, a:1, s:1, b:1),
% 4.21/4.56 skol10 [273, 2] (w:1, o:235, a:1, s:1, b:1),
% 4.21/4.56 skol11 [274, 1] (w:1, o:118, a:1, s:1, b:1),
% 4.21/4.56 skol12 [275, 2] (w:1, o:236, a:1, s:1, b:1),
% 4.21/4.56 skol13 [276, 3] (w:1, o:283, a:1, s:1, b:1),
% 4.21/4.56 skol14 [277, 1] (w:1, o:119, a:1, s:1, b:1),
% 4.21/4.56 skol15 [278, 2] (w:1, o:237, a:1, s:1, b:1),
% 4.21/4.56 skol16 [279, 2] (w:1, o:238, a:1, s:1, b:1),
% 4.21/4.56 skol17 [280, 3] (w:1, o:284, a:1, s:1, b:1),
% 4.21/4.56 skol18 [281, 2] (w:1, o:239, a:1, s:1, b:1),
% 4.21/4.56 skol19 [282, 1] (w:1, o:120, a:1, s:1, b:1),
% 4.21/4.56 skol20 [283, 2] (w:1, o:240, a:1, s:1, b:1),
% 4.21/4.56 skol21 [284, 2] (w:1, o:241, a:1, s:1, b:1),
% 4.21/4.56 skol22 [285, 2] (w:1, o:242, a:1, s:1, b:1),
% 4.21/4.56 skol23 [286, 2] (w:1, o:243, a:1, s:1, b:1),
% 4.21/4.56 skol24 [287, 3] (w:1, o:288, a:1, s:1, b:1),
% 4.21/4.56 skol25 [288, 2] (w:1, o:244, a:1, s:1, b:1),
% 4.21/4.56 skol26 [289, 1] (w:1, o:121, a:1, s:1, b:1),
% 4.21/4.56 skol27 [290, 2] (w:1, o:245, a:1, s:1, b:1),
% 23.41/23.78 skol28 [291, 3] (w:1, o:289, a:1, s:1, b:1),
% 23.41/23.78 skol29 [292, 3] (w:1, o:290, a:1, s:1, b:1),
% 23.41/23.78 skol30 [293, 2] (w:1, o:227, a:1, s:1, b:1),
% 23.41/23.78 skol31 [294, 3] (w:1, o:291, a:1, s:1, b:1),
% 23.41/23.78 skol32 [295, 2] (w:1, o:228, a:1, s:1, b:1),
% 23.41/23.78 skol33 [296, 2] (w:1, o:229, a:1, s:1, b:1),
% 23.41/23.78 skol34 [297, 3] (w:1, o:292, a:1, s:1, b:1),
% 23.41/23.78 skol35 [298, 3] (w:1, o:293, a:1, s:1, b:1),
% 23.41/23.78 skol36 [299, 2] (w:1, o:230, a:1, s:1, b:1),
% 23.41/23.78 skol37 [300, 2] (w:1, o:231, a:1, s:1, b:1).
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Starting Search:
% 23.41/23.78
% 23.41/23.78 *** allocated 113905 integers for clauses
% 23.41/23.78 *** allocated 170857 integers for clauses
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 3019
% 23.41/23.78 Kept: 2001
% 23.41/23.78 Inuse: 56
% 23.41/23.78 Deleted: 1
% 23.41/23.78 Deletedinuse: 0
% 23.41/23.78
% 23.41/23.78 *** allocated 256285 integers for clauses
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 *** allocated 170857 integers for termspace/termends
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 6441
% 23.41/23.78 Kept: 4008
% 23.41/23.78 Inuse: 198
% 23.41/23.78 Deleted: 2
% 23.41/23.78 Deletedinuse: 0
% 23.41/23.78
% 23.41/23.78 *** allocated 384427 integers for clauses
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 *** allocated 256285 integers for termspace/termends
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 12302
% 23.41/23.78 Kept: 6061
% 23.41/23.78 Inuse: 253
% 23.41/23.78 Deleted: 3
% 23.41/23.78 Deletedinuse: 0
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 *** allocated 576640 integers for clauses
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 17279
% 23.41/23.78 Kept: 8078
% 23.41/23.78 Inuse: 314
% 23.41/23.78 Deleted: 3
% 23.41/23.78 Deletedinuse: 0
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 22129
% 23.41/23.78 Kept: 10113
% 23.41/23.78 Inuse: 348
% 23.41/23.78 Deleted: 3
% 23.41/23.78 Deletedinuse: 0
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 *** allocated 384427 integers for termspace/termends
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 *** allocated 864960 integers for clauses
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 27364
% 23.41/23.78 Kept: 12674
% 23.41/23.78 Inuse: 412
% 23.41/23.78 Deleted: 4
% 23.41/23.78 Deletedinuse: 0
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 33025
% 23.41/23.78 Kept: 15110
% 23.41/23.78 Inuse: 446
% 23.41/23.78 Deleted: 5
% 23.41/23.78 Deletedinuse: 0
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 37425
% 23.41/23.78 Kept: 17144
% 23.41/23.78 Inuse: 500
% 23.41/23.78 Deleted: 6
% 23.41/23.78 Deletedinuse: 0
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 *** allocated 576640 integers for termspace/termends
% 23.41/23.78 *** allocated 1297440 integers for clauses
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 43798
% 23.41/23.78 Kept: 19590
% 23.41/23.78 Inuse: 539
% 23.41/23.78 Deleted: 7
% 23.41/23.78 Deletedinuse: 0
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 Resimplifying clauses:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 48947
% 23.41/23.78 Kept: 22327
% 23.41/23.78 Inuse: 574
% 23.41/23.78 Deleted: 310
% 23.41/23.78 Deletedinuse: 2
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 53746
% 23.41/23.78 Kept: 25453
% 23.41/23.78 Inuse: 599
% 23.41/23.78 Deleted: 310
% 23.41/23.78 Deletedinuse: 2
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 57404
% 23.41/23.78 Kept: 28133
% 23.41/23.78 Inuse: 614
% 23.41/23.78 Deleted: 310
% 23.41/23.78 Deletedinuse: 2
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 *** allocated 1946160 integers for clauses
% 23.41/23.78 *** allocated 864960 integers for termspace/termends
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 61428
% 23.41/23.78 Kept: 30136
% 23.41/23.78 Inuse: 655
% 23.41/23.78 Deleted: 310
% 23.41/23.78 Deletedinuse: 2
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 64463
% 23.41/23.78 Kept: 32298
% 23.41/23.78 Inuse: 659
% 23.41/23.78 Deleted: 310
% 23.41/23.78 Deletedinuse: 2
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 69108
% 23.41/23.78 Kept: 35281
% 23.41/23.78 Inuse: 679
% 23.41/23.78 Deleted: 310
% 23.41/23.78 Deletedinuse: 2
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 73023
% 23.41/23.78 Kept: 37292
% 23.41/23.78 Inuse: 715
% 23.41/23.78 Deleted: 310
% 23.41/23.78 Deletedinuse: 2
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 77062
% 23.41/23.78 Kept: 39323
% 23.41/23.78 Inuse: 746
% 23.41/23.78 Deleted: 310
% 23.41/23.78 Deletedinuse: 2
% 23.41/23.78
% 23.41/23.78 Resimplifying inuse:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78 Resimplifying clauses:
% 23.41/23.78 Done
% 23.41/23.78
% 23.41/23.78
% 23.41/23.78 Intermediate Status:
% 23.41/23.78 Generated: 82254
% 23.41/23.78 Kept: 42937
% 23.41/23.78 Inuse: 764
% 23.41/23.78 Deleted: 422
% 23.41/23.78 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 *** allocated 2919240 integers for clauses
% 78.31/78.73 *** allocated 1297440 integers for termspace/termends
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 86176
% 78.31/78.73 Kept: 45008
% 78.31/78.73 Inuse: 794
% 78.31/78.73 Deleted: 422
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 89284
% 78.31/78.73 Kept: 47212
% 78.31/78.73 Inuse: 804
% 78.31/78.73 Deleted: 422
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 95221
% 78.31/78.73 Kept: 49301
% 78.31/78.73 Inuse: 839
% 78.31/78.73 Deleted: 422
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 99658
% 78.31/78.73 Kept: 51319
% 78.31/78.73 Inuse: 863
% 78.31/78.73 Deleted: 422
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 104946
% 78.31/78.73 Kept: 53372
% 78.31/78.73 Inuse: 889
% 78.31/78.73 Deleted: 422
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 111843
% 78.31/78.73 Kept: 57280
% 78.31/78.73 Inuse: 914
% 78.31/78.73 Deleted: 422
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 115945
% 78.31/78.73 Kept: 60010
% 78.31/78.73 Inuse: 924
% 78.31/78.73 Deleted: 422
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying clauses:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 120320
% 78.31/78.73 Kept: 62038
% 78.31/78.73 Inuse: 944
% 78.31/78.73 Deleted: 484
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 124805
% 78.31/78.73 Kept: 64062
% 78.31/78.73 Inuse: 965
% 78.31/78.73 Deleted: 484
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 *** allocated 4378860 integers for clauses
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 129747
% 78.31/78.73 Kept: 66079
% 78.31/78.73 Inuse: 985
% 78.31/78.73 Deleted: 484
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 *** allocated 1946160 integers for termspace/termends
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 134796
% 78.31/78.73 Kept: 68095
% 78.31/78.73 Inuse: 1010
% 78.31/78.73 Deleted: 484
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 145103
% 78.31/78.73 Kept: 71652
% 78.31/78.73 Inuse: 1027
% 78.31/78.73 Deleted: 484
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 148704
% 78.31/78.73 Kept: 74527
% 78.31/78.73 Inuse: 1034
% 78.31/78.73 Deleted: 484
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 154951
% 78.31/78.73 Kept: 76545
% 78.31/78.73 Inuse: 1056
% 78.31/78.73 Deleted: 484
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 164539
% 78.31/78.73 Kept: 78657
% 78.31/78.73 Inuse: 1079
% 78.31/78.73 Deleted: 484
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying clauses:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 173247
% 78.31/78.73 Kept: 80659
% 78.31/78.73 Inuse: 1089
% 78.31/78.73 Deleted: 2205
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 189108
% 78.31/78.73 Kept: 83495
% 78.31/78.73 Inuse: 1099
% 78.31/78.73 Deleted: 2205
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 196576
% 78.31/78.73 Kept: 85503
% 78.31/78.73 Inuse: 1136
% 78.31/78.73 Deleted: 2205
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 208777
% 78.31/78.73 Kept: 89243
% 78.31/78.73 Inuse: 1162
% 78.31/78.73 Deleted: 2207
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 *** allocated 2919240 integers for termspace/termends
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 216172
% 78.31/78.73 Kept: 92240
% 78.31/78.73 Inuse: 1172
% 78.31/78.73 Deleted: 2207
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 222327
% 78.31/78.73 Kept: 94263
% 78.31/78.73 Inuse: 1203
% 78.31/78.73 Deleted: 2207
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 227161
% 78.31/78.73 Kept: 97315
% 78.31/78.73 Inuse: 1212
% 78.31/78.73 Deleted: 2207
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 *** allocated 6568290 integers for clauses
% 78.31/78.73
% 78.31/78.73 Intermediate Status:
% 78.31/78.73 Generated: 232071
% 78.31/78.73 Kept: 100253
% 78.31/78.73 Inuse: 1222
% 78.31/78.73 Deleted: 2207
% 78.31/78.73 Deletedinuse: 2
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying clauses:
% 78.31/78.73 Done
% 78.31/78.73
% 78.31/78.73 Resimplifying inuse:
% 78.31/78.73 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 237682
% 191.59/192.01 Kept: 102416
% 191.59/192.01 Inuse: 1257
% 191.59/192.01 Deleted: 2223
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 243394
% 191.59/192.01 Kept: 104432
% 191.59/192.01 Inuse: 1294
% 191.59/192.01 Deleted: 2223
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 249561
% 191.59/192.01 Kept: 106490
% 191.59/192.01 Inuse: 1327
% 191.59/192.01 Deleted: 2223
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 262800
% 191.59/192.01 Kept: 108787
% 191.59/192.01 Inuse: 1332
% 191.59/192.01 Deleted: 2223
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 280509
% 191.59/192.01 Kept: 112166
% 191.59/192.01 Inuse: 1347
% 191.59/192.01 Deleted: 2223
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 285928
% 191.59/192.01 Kept: 114179
% 191.59/192.01 Inuse: 1364
% 191.59/192.01 Deleted: 2223
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 314846
% 191.59/192.01 Kept: 117366
% 191.59/192.01 Inuse: 1367
% 191.59/192.01 Deleted: 2223
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 322277
% 191.59/192.01 Kept: 119472
% 191.59/192.01 Inuse: 1382
% 191.59/192.01 Deleted: 2223
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying clauses:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 327663
% 191.59/192.01 Kept: 121513
% 191.59/192.01 Inuse: 1402
% 191.59/192.01 Deleted: 2401
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 335152
% 191.59/192.01 Kept: 123515
% 191.59/192.01 Inuse: 1431
% 191.59/192.01 Deleted: 2401
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 *** allocated 4378860 integers for termspace/termends
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 362755
% 191.59/192.01 Kept: 127018
% 191.59/192.01 Inuse: 1452
% 191.59/192.01 Deleted: 2401
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 396839
% 191.59/192.01 Kept: 131013
% 191.59/192.01 Inuse: 1462
% 191.59/192.01 Deleted: 2401
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 408837
% 191.59/192.01 Kept: 133040
% 191.59/192.01 Inuse: 1473
% 191.59/192.01 Deleted: 2401
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 418068
% 191.59/192.01 Kept: 135133
% 191.59/192.01 Inuse: 1502
% 191.59/192.01 Deleted: 2401
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 426021
% 191.59/192.01 Kept: 137368
% 191.59/192.01 Inuse: 1532
% 191.59/192.01 Deleted: 2401
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 433255
% 191.59/192.01 Kept: 139370
% 191.59/192.01 Inuse: 1561
% 191.59/192.01 Deleted: 2401
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying clauses:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 440013
% 191.59/192.01 Kept: 141452
% 191.59/192.01 Inuse: 1587
% 191.59/192.01 Deleted: 2609
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 447284
% 191.59/192.01 Kept: 144119
% 191.59/192.01 Inuse: 1597
% 191.59/192.01 Deleted: 2609
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 455732
% 191.59/192.01 Kept: 146925
% 191.59/192.01 Inuse: 1612
% 191.59/192.01 Deleted: 2609
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 465101
% 191.59/192.01 Kept: 148938
% 191.59/192.01 Inuse: 1649
% 191.59/192.01 Deleted: 2609
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 *** allocated 9852435 integers for clauses
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 472697
% 191.59/192.01 Kept: 151252
% 191.59/192.01 Inuse: 1677
% 191.59/192.01 Deleted: 2609
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 478714
% 191.59/192.01 Kept: 153307
% 191.59/192.01 Inuse: 1707
% 191.59/192.01 Deleted: 2609
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 485881
% 191.59/192.01 Kept: 155572
% 191.59/192.01 Inuse: 1737
% 191.59/192.01 Deleted: 2609
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01
% 191.59/192.01 Intermediate Status:
% 191.59/192.01 Generated: 493228
% 191.59/192.01 Kept: 157698
% 191.59/192.01 Inuse: 1772
% 191.59/192.01 Deleted: 2609
% 191.59/192.01 Deletedinuse: 2
% 191.59/192.01
% 191.59/192.01 Resimplifying inuse:
% 191.59/192.01 Done
% 191.59/192.01
% 191.59/192.01 ResiCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------