TSTP Solution File: SWW237+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW237+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 23:21:28 EDT 2022
% Result : Timeout 300.08s 300.58s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW237+1 : TPTP v8.1.0. Released v5.2.0.
% 0.13/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n023.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
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Sun Jun 5 11:24:09 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.98/1.59 *** allocated 10000 integers for termspace/termends
% 0.98/1.59 *** allocated 10000 integers for clauses
% 0.98/1.59 *** allocated 10000 integers for justifications
% 0.98/1.59 *** allocated 15000 integers for termspace/termends
% 0.98/1.59 *** allocated 22500 integers for termspace/termends
% 0.98/1.59 *** allocated 33750 integers for termspace/termends
% 0.98/1.59 Bliksem 1.12
% 0.98/1.59
% 0.98/1.59
% 0.98/1.59 Automatic Strategy Selection
% 0.98/1.59
% 0.98/1.59 *** allocated 50625 integers for termspace/termends
% 0.98/1.59 *** allocated 75937 integers for termspace/termends
% 0.98/1.59 *** allocated 113905 integers for termspace/termends
% 0.98/1.59
% 0.98/1.59 Clauses:
% 0.98/1.59
% 0.98/1.59 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.98/1.59 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.59 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.98/1.59 , Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.59 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.98/1.59 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.98/1.59 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.98/1.59 ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.98/1.59 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.59 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.59 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.59 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.59 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.59 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ) ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.98/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.59 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.59 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.98/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.59 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.59 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.59 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Z, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Y, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.59 .
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.59 .
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.59 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.98/1.59 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.98/1.59 hAPP( Y, U ) ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.98/1.59 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.59 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.98/1.59 hAPP( Y, U ) ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.98/1.59 ( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.98/1.59 ( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.98/1.59 hAPP( Y, U ) ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.98/1.59 ( Z, skol2( X, Y, Z ) ), hAPP( Y, skol2( X, Y, Z ) ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.98/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Y, T ), Z = Y }.
% 0.98/1.59 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 T, Y ), Z = Y }.
% 0.98/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 T, Y ), Z = Y }.
% 0.98/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Y, Z ), T = Y }.
% 0.98/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Y, Z ) }.
% 0.98/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 T, Y ), Z = Y }.
% 0.98/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 T, Y ) }.
% 0.98/1.59 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.59 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.98/1.59 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.59 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ) ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.59 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.59 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.98/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.59 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.98/1.59 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.59 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.98/1.59 { ! c_Polynomial_OpCons( tc_Complex_Ocomplex, v_c____, v_cs____ ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.98/1.59 }.
% 0.98/1.59 { ! v_c____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), !
% 0.98/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ),
% 0.98/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.98/1.59 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z )
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) ) ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.98/1.59 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ),
% 0.98/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( tc_RealDef_Oreal, Z, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.98/1.59 , X ) ) ) ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.59 ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.59 ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.59 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.98/1.59 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.98/1.59 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.98/1.59 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.98/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.98/1.59 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.98/1.59 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.59 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Y ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.59 , Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.59 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.98/1.59 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! Y = Z }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! Z = Y }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! Z = Y }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.59 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.59 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.59 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ), Z ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Z ), Y ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.60 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.60 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), ! Z = Y }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 Z ), ! Z = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.98/1.60 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.98/1.60 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.98/1.60 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.98/1.60 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.60 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 Z, Y ) ) = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.60 Y ) ) = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.98/1.60 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.98/1.60 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , ! Z = Y }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.60 , T ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , T, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , Y, T ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , T, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , Y, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.60 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.98/1.60 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.98/1.60 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.98/1.60 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.98/1.60 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ), Y ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Z ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 Z ) = Y }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.98/1.60 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.98/1.60 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.98/1.60 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.60 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , Y, T ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.98/1.60 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ) }.
% 0.98/1.60 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_RealDef_Oreal, Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.98/1.60 , X ) ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 X, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , c_Groups_Oabs__class_Oabs( X, Y ) ), c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.60 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.98/1.60 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha1
% 0.98/1.60 ( X, Y, Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.60 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! alpha1( X, Y, Z ),
% 0.98/1.60 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.98/1.60 { ! alpha1( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.60 alpha1( X, Y, Z ) }.
% 0.98/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_c____ ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.98/1.60 ( tc_RealDef_Oreal, v_da____ ), c_RealVector_Onorm__class_Onorm(
% 0.98/1.60 tc_Complex_Ocomplex, v_aa____ ) ), c_RealVector_Onorm__class_Onorm(
% 0.98/1.60 tc_Complex_Ocomplex, v_c____ ) ), c_RealVector_Onorm__class_Onorm(
% 0.98/1.60 tc_Complex_Ocomplex, v_z____ ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.98/1.60 , X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.60 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.60 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.60 { alpha55( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.60 { alpha55( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.98/1.60 ( X, Y ), Z ) ) }.
% 0.98/1.60 { ! alpha55( X, Y, Z ), alpha57( X, Y, Z ), Z = Y }.
% 0.98/1.60 { ! alpha55( X, Y, Z ), alpha57( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! alpha57( X, Y, Z ), alpha55( X, Y, Z ) }.
% 0.98/1.60 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha55( X, Y, Z ) }.
% 0.98/1.60 { ! alpha57( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.98/1.60 }.
% 0.98/1.60 { ! alpha57( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.98/1.60 X, Y ), Z ) ), alpha57( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol3( X, Y ) ) }.
% 0.98/1.60 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.60 ), Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.60 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha2( X, Y
% 0.98/1.60 ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha24( X,
% 0.98/1.60 Y ) }.
% 0.98/1.60 { ! alpha2( X, Y ), ! alpha24( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 0.98/1.60 { ! alpha24( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha24( X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha24( X, Y ) }.
% 0.98/1.60 { ! alpha2( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha2( X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha2( X, Y ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Y ) = Y }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.60 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, Z ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), X ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ) ) = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), X ) = X }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ), Z = Y }.
% 0.98/1.60 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) }.
% 0.98/1.60 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.98/1.60 ( tc_RealDef_Oreal, v_da____ ), c_RealVector_Onorm__class_Onorm(
% 0.98/1.60 tc_Complex_Ocomplex, v_aa____ ) ), c_RealVector_Onorm__class_Onorm(
% 0.98/1.60 tc_Complex_Ocomplex, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Complex_Ocomplex ), v_z____ ), v_c____ ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.98/1.60 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.98/1.60 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.60 ( X, Y ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.60 ( X, Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z ), Y
% 0.98/1.60 ) = c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.60 , Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.98/1.60 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.60 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.98/1.60 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.98/1.60 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.98/1.60 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.60 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.60 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.98/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.98/1.60 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.60 ), U = Z, T = Y }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.98/1.60 ) ), Z ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.60 ), ! U = T }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.60 ), ! Z = Y }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.98/1.60 ) ), T ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.60 ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.60 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.60 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.60 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.98/1.60 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.98/1.60 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha25( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha3( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha25( X, Y, Z, T ), !
% 0.98/1.60 alpha3( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.98/1.60 { ! alpha25( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.98/1.60 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha25( X, Y, Z, T ) }.
% 0.98/1.60 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha25(
% 0.98/1.60 X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha3( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha26( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha4( X, Y, T ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha26( X, Y, Z, T ), !
% 0.98/1.60 alpha4( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.60 { ! alpha26( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha26( X, Y, Z, T ) }.
% 0.98/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha26(
% 0.98/1.60 X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha4( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { Y = c_Groups_Ozero__class_Ozero( X ), alpha4( X, Y, Z ) }.
% 0.98/1.60 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha4( X, Y, Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha5( X, Y
% 0.98/1.60 , Z ), alpha27( X, Y, Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha27( X, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha27( X, Y, Z ) }.
% 0.98/1.60 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.60 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), alpha5( X, Y, Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ), alpha6( X, Y, Z ), alpha28( X, Y, Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha28( X, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ), Y ), alpha28( X, Y, Z ) }.
% 0.98/1.60 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.60 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha6( X, Y, Z ) }.
% 0.98/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 Z, Y ) ), alpha29( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 Z, Y ) ), alpha43( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha29( X, Y, Z
% 0.98/1.60 , T ), ! alpha43( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.60 { ! alpha43( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), alpha47( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.60 , alpha43( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha47( X, Y, Z, T ), alpha43( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha47( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha47( X, Y, Z, T ), alpha7( X, Y, T ) }.
% 0.98/1.60 { ! alpha51( X, Y, Z, T ), ! alpha7( X, Y, T ), alpha47( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha51( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 alpha51( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha51( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha29( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 alpha29( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha29( X, Y, Z, T )
% 0.98/1.60 }.
% 0.98/1.60 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , alpha7( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , alpha7( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Z ), Y ), alpha30( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Z ), Y ), alpha44( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha30( X, Y, Z
% 0.98/1.60 , T ), ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.98/1.60 { ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), alpha48( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , alpha44( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha48( X, Y, Z, T ), alpha44( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha48( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha48( X, Y, Z, T ), alpha8( X, Y, Z ) }.
% 0.98/1.60 { ! alpha52( X, Y, Z, T ), ! alpha8( X, Y, Z ), alpha48( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha52( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 alpha52( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha52( X, Y, Z, T )
% 0.98/1.60 }.
% 0.98/1.60 { ! alpha30( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.60 alpha30( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha30( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , alpha8( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.60 , alpha8( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha9( X, Y, Z, T ),
% 0.98/1.60 alpha31( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha31( X, Y, Z, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha31( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.60 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha9( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha10( X, Y, Z, T ),
% 0.98/1.60 alpha32( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha32( X, Y, Z, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha32( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.98/1.60 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha10( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.60 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.98/1.60 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ), alpha33( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ), alpha45( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha33( X, Y, Z
% 0.98/1.60 , T ), ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.60 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), alpha49( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.60 , alpha45( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha49( X, Y, Z, T ), alpha45( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha49( X, Y, Z, T ), alpha53( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha49( X, Y, Z, T ), alpha11( X, Y, T ) }.
% 0.98/1.60 { ! alpha53( X, Y, Z, T ), ! alpha11( X, Y, T ), alpha49( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha53( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 alpha53( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha53( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha33( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 alpha33( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha33( X, Y, Z, T )
% 0.98/1.60 }.
% 0.98/1.60 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , alpha11( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ), alpha11( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Z ), Y ), alpha34( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Z ), Y ), alpha46( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha34( X, Y, Z
% 0.98/1.60 , T ), ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.98/1.60 { ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), alpha50( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , alpha46( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha50( X, Y, Z, T ), alpha46( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha50( X, Y, Z, T ), alpha54( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha50( X, Y, Z, T ), alpha12( X, Y, Z ) }.
% 0.98/1.60 { ! alpha54( X, Y, Z, T ), ! alpha12( X, Y, Z ), alpha50( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha54( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 alpha54( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha54( X, Y, Z, T )
% 0.98/1.60 }.
% 0.98/1.60 { ! alpha34( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.60 alpha34( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha34( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , alpha12( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , Y ), alpha12( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring__abs( X ), alpha56( X, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring__abs( X ), alpha56( X, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.60 { ! alpha56( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! alpha56( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ), alpha56( X, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.98/1.60 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.60 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.60 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.60 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.60 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.60 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z, Y )
% 0.98/1.60 ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.98/1.60 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.98/1.60 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha13( X, Y, Z ), alpha35
% 0.98/1.60 ( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha13( X, Y, Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.60 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha35( X, Y, Z ) }.
% 0.98/1.60 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.60 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), alpha13( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ), alpha36
% 0.98/1.60 ( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha14( X, Y, Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ), Y ), alpha36( X, Y, Z ) }.
% 0.98/1.60 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.60 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha15( X, Y, Z ), alpha37
% 0.98/1.60 ( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha15( X, Y, Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.60 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), alpha37( X, Y, Z ) }.
% 0.98/1.60 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.60 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), alpha15( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.98/1.60 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha16( X, Y, Z ), alpha38( X,
% 0.98/1.60 Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha16( X, Y, Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), alpha38( X, Y, Z ) }.
% 0.98/1.60 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.60 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), alpha16( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , Y, Z ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , Y, Z ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.60 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs(
% 0.98/1.60 X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_RealDef_Oreal ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.98/1.60 class_RealVector_Oreal__normed__field( X ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.60 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.60 ( X, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.98/1.60 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.60 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.60 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.60 tc_Complex_Ocomplex ) ), ! c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 tc_RealDef_Oreal, skol4, c_RealVector_Onorm__class_Onorm(
% 0.98/1.60 tc_Complex_Ocomplex, X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(
% 0.98/1.60 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.98/1.60 c_Polynomial_OpCons( tc_Complex_Ocomplex, v_aa____, c_Polynomial_OpCons(
% 0.98/1.60 tc_Complex_Ocomplex, v_c____, v_cs____ ) ) ), X ) ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.98/1.60 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.98/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.98/1.60 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.98/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.98/1.60 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.98/1.60 .
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.98/1.60 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.98/1.60 .
% 0.98/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.98/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.98/1.60 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.98/1.60 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.98/1.60 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.60 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.60 Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.98/1.60 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.98/1.60 ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.98/1.60 ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.98/1.60 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.60 tc_Complex_Ocomplex ) ), ! c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 tc_RealDef_Oreal, skol5( X, Y ), c_RealVector_Onorm__class_Onorm(
% 0.98/1.60 tc_Complex_Ocomplex, Z ) ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 tc_RealDef_Oreal, Y, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.98/1.60 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.98/1.60 tc_Complex_Ocomplex, X, v_cs____ ) ), Z ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.98/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol6( X, Y ) ) }.
% 0.98/1.60 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.98/1.60 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.98/1.60 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.98/1.60 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.98/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.98/1.60 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.98/1.60 .
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7( Z, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.60 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol7( X, Y ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol8( Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol8( X ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol9( Z, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol9( X, Y ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10( Z, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol10( X, Y ) ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol11( Z, T ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol11( X, Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol12( Z, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.60 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol12( X, Y ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol13( Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol13( X ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol14( Z, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol14( X, Y ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol15( Z, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol15( X, Y ) ) ) }.
% 0.98/1.60 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 0.98/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.60 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.60 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol16( X, Y ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol17( X, Y ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol18( X ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol19( X, Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.98/1.60 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.60 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.60 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.98/1.60 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.60 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.98/1.60 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.60 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.60 , Y ), X ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.98/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Nat_Onat ) }.
% 0.98/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Nat_Onat ) }.
% 0.98/1.60 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.60 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.98/1.61 ( X ) }.
% 0.98/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.98/1.61 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.98/1.61 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.61 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.98/1.61 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.98/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.98/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.98/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.61 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.98/1.61 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.61 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.98/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.61 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.98/1.61 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.61 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.98/1.61 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.98/1.61 , X ) }.
% 0.98/1.61 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Orcis( Y
% 0.98/1.61 , X ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 0.98/1.61 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.98/1.61 ), Y ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.98/1.61 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.98/1.61 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.98/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.61 skol20( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, skol20( X, T, U ),
% 0.98/1.61 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.61 , Y ) }.
% 0.98/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), skol20( X, Y, Z ) ), Z ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.61 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.61 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.98/1.61 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.61 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 X ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.98/1.61 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.61 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.61 Z, T ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oabs__class_Oabs( X, Z )
% 0.98/1.61 = c_Groups_Oabs__class_Oabs( X, Y ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.61 c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.61 ), c_Rings_Odvd__class_Odvd( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.61 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oabs__class_Oabs( X, Y ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.61 , Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.61 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.98/1.61 , Z, Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.61 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.61 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.98/1.61 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.98/1.61 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.98/1.61 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.98/1.61 hAPP( Z, skol21( U, W, Z ) ) ) }.
% 0.98/1.61 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.98/1.61 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol21( X
% 0.98/1.61 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.98/1.61 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.98/1.61 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol32( X,
% 0.98/1.61 Y, Z ) ) ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.98/1.61 ( X ) ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.98/1.61 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.98/1.61 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.61 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.98/1.61 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.61 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Nat_Onat ) ) = Y }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.98/1.61 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.98/1.61 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.98/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.98/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.61 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.98/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.98/1.61 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.98/1.61 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, Z, Y ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.98/1.61 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.61 X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.98/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.98/1.61 ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.61 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.98/1.61 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.61 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.98/1.61 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.61 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_RealDef_Oreal ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_RealDef_Oreal ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.98/1.61 ( X ), Y ), Z ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.98/1.61 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.98/1.61 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.61 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.98/1.61 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha17( X, Y ), Y = X }
% 0.98/1.61 .
% 0.98/1.61 { ! alpha17( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! alpha17( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! alpha17( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), alpha17( X, Y ) }.
% 0.98/1.61 { ! alpha18( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! alpha18( X, Y ), ! Y = X }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha18( X, Y ) }
% 0.98/1.61 .
% 0.98/1.61 { ! alpha18( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! alpha18( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), alpha18( X, Y ) }.
% 0.98/1.61 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.61 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.61 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Nat_Onat, Y, Z ) }.
% 0.98/1.61 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Nat_Onat, Y, Z ) }.
% 0.98/1.61 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.98/1.61 , Z ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.98/1.61 Z, Y ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Nat_Onat, Y, Z ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.98/1.61 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.98/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.98/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.98/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.98/1.61 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.61 ), X ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.98/1.61 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.98/1.61 ) }.
% 0.98/1.61 { c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X,
% 0.98/1.61 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( X ) }.
% 0.98/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.61 = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.98/1.61 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.98/1.61 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.98/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Nat_Onat ) ) = Y }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.61 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.98/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) }.
% 0.98/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.61 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.98/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.98/1.61 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.98/1.61 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.61 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.98/1.61 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.61 ), T ), U ), Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.61 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.61 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.98/1.61 ( hAPP( c_Power_Opower__class_Opower( X ),
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) =
% 0.98/1.61 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.61 ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.98/1.61 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.61 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.61 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.98/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.61 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.61 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.98/1.61 ) ) }.
% 0.98/1.61 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.61 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.98/1.61 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.98/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.98/1.61 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol22( X, Y ) ), Y
% 0.98/1.61 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), Y ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.98/1.61 Y ) ) ), Y ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.61 X ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.61 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) = c_Groups_Oone__class_Oone
% 0.98/1.61 ( tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ),
% 0.98/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.98/1.61 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.98/1.61 ) ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Int_Oint, Y, X ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.98/1.61 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.98/1.61 , Z ), X ) ), T ) ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, U, T ) ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.98/1.61 ( tc_Int_Oint, Y ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.98/1.61 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.98/1.61 ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), c_Groups_Oabs__class_Oabs
% 0.98/1.61 ( tc_Int_Oint, Y ) = c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.98/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.98/1.61 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.98/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.98/1.61 tc_Int_Oint, Y ) ), X ) ) }.
% 0.98/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.98/1.61 ( tc_Int_Oint ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.98/1.61 }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.98/1.61 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.98/1.61 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.98/1.61 = X }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ) ) }.
% 0.98/1.61 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.98/1.61 }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.98/1.61 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.98/1.61 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.61 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.61 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.98/1.61 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.98/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.61 X ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.98/1.61 .
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.98/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.98/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.98/1.61 ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.98/1.61 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.98/1.61 }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.98/1.61 c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.98/1.61 ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.98/1.61 , c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.98/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.98/1.61 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.98/1.61 { ! c_Nat_OSuc( X ) = X }.
% 0.98/1.61 { ! X = c_Nat_OSuc( X ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.98/1.61 .
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.61 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ) ) = X }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), X ) = X }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.98/1.61 tc_Int_Oint, X ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.98/1.61 tc_Int_Oint, X ) = X }.
% 0.98/1.61 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.98/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.98/1.61 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.98/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.61 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.61 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.61 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.61 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol23( X ) ) }.
% 0.98/1.61 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha19( X, Y ) }.
% 0.98/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! alpha19( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.61 c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! alpha19( X, Y ), Y = c_Nat_OSuc( skol24( Z, Y ) ) }.
% 0.98/1.61 { ! alpha19( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol24( X
% 0.98/1.61 , Y ), X ) }.
% 0.98/1.61 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.98/1.61 ), alpha19( X, Y ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.61 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha20( X, Y ),
% 0.98/1.61 alpha39( X, Y ) }.
% 0.98/1.61 { ! alpha20( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! alpha39( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! alpha39( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! alpha39( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha39( X, Y ) }.
% 0.98/1.61 { ! alpha20( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! alpha20( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha20( X, Y ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ), alpha40( X
% 0.98/1.61 , Y ) }.
% 0.98/1.61 { ! alpha21( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! alpha40( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! alpha40( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! alpha40( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha40( X, Y ) }.
% 0.98/1.61 { ! alpha21( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! alpha21( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha21( X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.98/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.98/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol25( X, Y ) ) ) }.
% 0.98/1.61 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.61 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.61 ), X ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.98/1.61 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.98/1.61 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.61 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.61 ), X ) ) }.
% 0.98/1.61 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.61 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 X ), Y ), Z = Y }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.61 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.61 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.98/1.61 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.98/1.61 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Int_Oint, Z, X ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.98/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.98/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.61 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.98/1.61 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Nat_Onat, Z, X ) }.
% 0.98/1.61 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Nat_Onat ), X ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.61 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.98/1.61 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.61 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.98/1.61 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.98/1.61 Y ) ) ), Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.61 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), Y ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.61 ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.98/1.61 ( tc_Int_Oint ), Y ) }.
% 0.98/1.61 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.61 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.61 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.61 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.61 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.61 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.61 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.98/1.61 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.61 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.98/1.61 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.98/1.61 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.98/1.61 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol26( Z, Y ) ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.98/1.61 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, skol26( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.61 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.98/1.61 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.98/1.61 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.98/1.61 ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.98/1.61 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.98/1.61 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.98/1.61 ) ) }.
% 0.98/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.98/1.61 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol27( Z, Y
% 0.98/1.61 ), Y ) }.
% 0.98/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.98/1.61 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.61 skol27( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.98/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.98/1.61 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.98/1.61 , skol27( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol28( Z, T ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol28( X, Y ) ), X ) =
% 0.98/1.61 Y }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( Z, T ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol29( X, Y ) ), X ) =
% 0.98/1.61 Y }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.98/1.61 skol29( X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.61 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.61 ( X, Y ) ) ) }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.61 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( X ) ) }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.61 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , Z, Y ) }.
% 0.98/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.98/1.61 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.98/1.61 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.61 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.98/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.98/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.61 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.98/1.61 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.61 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.61 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.61 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.61 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.98/1.61 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.61 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.61 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.98/1.61 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.98/1.61 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.98/1.61 hAPP( Z, Y ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.98/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.61 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( X, Y, Z ) ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.61 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.98/1.61 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.98/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.61 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.61 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.98/1.61 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.61 Y ) ) ) ) }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.98/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.98/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.61 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.61 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.61 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.98/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.98/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.61 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.98/1.61 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( X, Z, W ) ), U ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.61 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.61 X, W, Z ) ), U ), T ), Y ) }.
% 0.98/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), Z ), U ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.98/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.61 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.61 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.61 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.98/1.61 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.61 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.98/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.98/1.61 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.61 , Y ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.98/1.61 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.61 X, Z, Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.61 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.61 X, Y ) ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.61 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.98/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.98/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.98/1.61 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.61 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.61 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.98/1.61 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.61 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.98/1.61 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.98/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.98/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.61 X, Y ) }.
% 0.98/1.61 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.61 Z ) ), U ), T ) = Y }.
% 0.98/1.61 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.61 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), Z ), U ), Y ) }.
% 0.98/1.61 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.61 W ) ), U ), Y ) }.
% 0.98/1.61 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.61 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), Z ), U ), Y ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.61 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.61 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.98/1.61 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.61 Z ) ), Y ) ) }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.98/1.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.98/1.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.98/1.61 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.98/1.61 ( tc_Int_Oint ) ) ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.61 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.61 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( X, T, Y ) ) ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.98/1.61 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.61 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.98/1.61 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( X, Z, Y ), T ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.98/1.61 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( X, Z, Y ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.98/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.98/1.61 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.98/1.61 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.98/1.61 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.61 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.98/1.61 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.98/1.61 ) ) = X }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.61 , ! alpha22( X, Y, Z ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.61 , ! alpha41( X, Y, Z ) }.
% 0.98/1.61 { alpha22( X, Y, Z ), alpha41( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.61 { ! alpha41( X, Y, Z ), ! hBOOL( hAPP( Z, skol30( T, U, Z ) ) ) }.
% 0.98/1.61 { ! alpha41( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.61 skol30( X, Y, Z ) ) }.
% 0.98/1.61 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.98/1.61 ) ), alpha41( X, Y, Z ) }.
% 0.98/1.61 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.98/1.61 }.
% 0.98/1.61 { ! alpha22( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha22( X, Y, Z ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.61 , alpha23( X, Y, Z ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.61 , alpha42( X, Y, Z ) }.
% 0.98/1.61 { ! alpha23( X, Y, Z ), ! alpha42( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.61 { ! alpha42( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.61 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, skol31( T, U, Z ) ) ), alpha42( X, Y, Z ) }.
% 0.98/1.61 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol31( X, Y, Z ) ),
% 0.98/1.61 alpha42( X, Y, Z ) }.
% 0.98/1.61 { ! alpha23( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.98/1.61 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha23( X, Y, Z ) }
% 0.98/1.61 .
% 0.98/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha23
% 0.98/1.61 ( X, Y, Z ) }.
% 0.98/1.61 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.98/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.98/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.61 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.61 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.61 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, Y ), hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.98/1.61 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), Y ) )
% 0.98/1.61 = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.98/1.61 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), X ) )
% 0.98/1.61 }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.98/1.61 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.61 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.98/1.61 ( tc_fun( Y, X ) ) }.
% 0.98/1.61 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.98/1.61 ) ) }.
% 0.98/1.61 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.98/1.61 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.98/1.61 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.98/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.61 tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.98/1.61 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.98/1.61 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.98/1.61 { class_Power_Opower( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.98/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.61 tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.98/1.61 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.98/1.61 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.98/1.61 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.98/1.61 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.98/1.61 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.98/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.61 tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.98/1.61 .
% 0.98/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Oabs__if( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 0.98/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.61 tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ),
% 0.98/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.98/1.61 ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.98/1.61 X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.98/1.61 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.98/1.61 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.98/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.98/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Groups_Oabs__if(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.98/1.61 ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.98/1.61 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, v_mzh,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, v_mazh, v_ma ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.98/1.61 ( tc_RealDef_Oreal, v_da____ ), v_ma ), v_mzh ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, v_da____, v_mazh )
% 0.98/1.61 }.
% 0.98/1.61
% 0.98/1.61 *** allocated 15000 integers for clauses
% 0.98/1.61 *** allocated 22500 integers for clauses
% 0.98/1.61 *** allocated 33750 integers for clauses
% 0.98/1.61 *** allocated 50625 integers for clauses
% 0.98/1.61 *** allocated 75937 integers for clauses
% 0.98/1.61 percentage equality = 0.232523, percentage horn = 0.901220
% 0.98/1.61 This is a problem with some equality
% 0.98/1.61
% 0.98/1.61
% 0.98/1.61
% 0.98/1.61 Options Used:
% 0.98/1.61
% 0.98/1.61 useres = 1
% 0.98/1.61 useparamod = 1
% 0.98/1.61 useeqrefl = 1
% 0.98/1.61 useeqfact = 1
% 0.98/1.61 usefactor = 1
% 0.98/1.61 usesimpsplitting = 0
% 0.98/1.61 usesimpdemod = 5
% 0.98/1.61 usesimpres = 3
% 0.98/1.61
% 0.98/1.61 resimpinuse = 1000
% 0.98/1.61 resimpclauses = 20000
% 0.98/1.61 substype = eqrewr
% 0.98/1.61 backwardsubs = 1
% 0.98/1.61 selectoldest = 5
% 0.98/1.61
% 0.98/1.61 litorderings [0] = split
% 0.98/1.61 litorderings [1] = extend the termordering, first sorting on arguments
% 0.98/1.61
% 0.98/1.61 termordering = kbo
% 0.98/1.61
% 0.98/1.61 litapriori = 0
% 0.98/1.61 termapriori = 1
% 0.98/1.61 litaposteriori = 0
% 0.98/1.61 termaposteriori = 0
% 0.98/1.61 demodaposteriori = 0
% 0.98/1.61 ordereqreflfact = 0
% 0.98/1.61
% 0.98/1.61 litselect = negord
% 0.98/1.61
% 0.98/1.61 maxweight = 15
% 0.98/1.61 maxdepth = 30000
% 0.98/1.61 maxlength = 115
% 0.98/1.61 maxnrvars = 195
% 0.98/1.61 excuselevel = 1
% 0.98/1.61 increasemaxweight = 1
% 0.98/1.61
% 0.98/1.61 maxselected = 10000000
% 0.98/1.61 maxnrclauses = 10000000
% 0.98/1.61
% 0.98/1.61 showgenerated = 0
% 0.98/1.61 showkept = 0
% 0.98/1.61 showselected = 0
% 0.98/1.61 showdeleted = 0
% 0.98/1.61 showresimp = 1
% 0.98/1.61 showstatus = 2000
% 0.98/1.61
% 0.98/1.61 prologoutput = 0
% 0.98/1.61 nrgoals = 5000000
% 0.98/1.61 totalproof = 1
% 0.98/1.61
% 0.98/1.61 Symbols occurring in the translation:
% 0.98/1.61
% 0.98/1.61 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.98/1.61 . [1, 2] (w:1, o:203, a:1, s:1, b:0),
% 0.98/1.61 ! [4, 1] (w:0, o:111, a:1, s:1, b:0),
% 0.98/1.61 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.98/1.61 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.98/1.61 hAPP [38, 2] (w:1, o:227, a:1, s:1, b:0),
% 0.98/1.61 v_p [39, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.98/1.61 tc_Complex_Ocomplex [40, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.98/1.61 tc_Polynomial_Opoly [41, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.98/1.61 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Oordered__ab__group__add__abs [46, 1] (w:1, o:126, a:1
% 0.98/1.61 , s:1, b:0),
% 0.98/1.61 c_Groups_Oplus__class_Oplus [47, 3] (w:1, o:269, a:1, s:1, b:0),
% 0.98/1.61 c_Groups_Oabs__class_Oabs [48, 2] (w:1, o:229, a:1, s:1, b:0),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq [49, 3] (w:1, o:270, a:1, s:1, b:0)
% 0.98/1.61 ,
% 0.98/1.61 class_Orderings_Opreorder [51, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.98/1.62 tc_RealDef_Oreal [54, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.98/1.62 class_Groups_Oordered__ab__semigroup__add__imp__le [58, 1] (w:1, o:
% 0.98/1.62 130, a:1, s:1, b:0),
% 0.98/1.62 class_Groups_Oordered__ab__semigroup__add [60, 1] (w:1, o:131, a:1
% 0.98/1.62 , s:1, b:0),
% 0.98/1.62 v_cs____ [62, 0] (w:1, o:37, a:1, s:1, b:0),
% 0.98/1.62 class_Groups_Ozero [64, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.98/1.62 class_Groups_Ocomm__monoid__add [65, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.98/1.62
% 0.98/1.62 class_Groups_Omonoid__add [66, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.98/1.62 class_Groups_Olinordered__ab__group__add [67, 1] (w:1, o:134, a:1, s:
% 0.98/1.62 1, b:0),
% 0.98/1.62 class_Groups_Oordered__comm__monoid__add [68, 1] (w:1, o:136, a:1, s:
% 0.98/1.62 1, b:0),
% 0.98/1.62 class_Orderings_Olinorder [70, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.98/1.62 class_Orderings_Oord [72, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.98/1.62 tc_fun [73, 2] (w:1, o:251, a:1, s:1, b:0),
% 0.98/1.62 class_Orderings_Oorder [74, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.98/1.62 class_Groups_Ocancel__semigroup__add [75, 1] (w:1, o:138, a:1, s:1
% 0.98/1.62 , b:0),
% 0.98/1.62 class_Groups_Ocancel__ab__semigroup__add [76, 1] (w:1, o:139, a:1, s:
% 0.98/1.62 1, b:0),
% 0.98/1.62 class_Groups_Oab__semigroup__add [77, 1] (w:1, o:140, a:1, s:1, b:0)
% 0.98/1.62 ,
% 0.98/1.62 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [82
% 0.98/1.62 , 1] (w:1, o:179, a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Ocomm__semiring__1 [83, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.98/1.62 v_c____ [86, 0] (w:1, o:49, a:1, s:1, b:0),
% 0.98/1.62 c_Polynomial_OpCons [87, 3] (w:1, o:273, a:1, s:1, b:0),
% 0.98/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [89, 2] (w:1, o:228
% 0.98/1.62 , a:1, s:1, b:0),
% 0.98/1.62 tc_Nat_Onat [90, 0] (w:1, o:50, a:1, s:1, b:0),
% 0.98/1.62 c_Polynomial_Opoly__rec [92, 5] (w:1, o:334, a:1, s:1, b:0),
% 0.98/1.62 c_Groups_Ouminus__class_Ouminus [95, 2] (w:1, o:252, a:1, s:1, b:0),
% 0.98/1.62
% 0.98/1.62 c_Orderings_Oord__class_Oless [96, 3] (w:1, o:271, a:1, s:1, b:0),
% 0.98/1.62 class_Groups_Oab__group__add [98, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.98/1.62 class_Groups_Oordered__ab__group__add [99, 1] (w:1, o:181, a:1, s:1
% 0.98/1.62 , b:0),
% 0.98/1.62 class_Groups_Ogroup__add [100, 1] (w:1, o:182, a:1, s:1, b:0),
% 0.98/1.62 c_fequal [102, 2] (w:1, o:253, a:1, s:1, b:0),
% 0.98/1.62 c_If [103, 4] (w:1, o:311, a:1, s:1, b:0),
% 0.98/1.62 class_Groups_Oabs__if [104, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.98/1.62 class_Groups_Oordered__cancel__ab__semigroup__add [105, 1] (w:1, o:
% 0.98/1.62 184, a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Olinordered__idom [106, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Olinordered__semidom [108, 1] (w:1, o:148, a:1, s:1, b:0)
% 0.98/1.62 ,
% 0.98/1.62 c_Polynomial_Opos__poly [110, 2] (w:1, o:254, a:1, s:1, b:0),
% 0.98/1.62 class_Lattices_Oboolean__algebra [111, 1] (w:1, o:186, a:1, s:1, b:0)
% 0.98/1.62 ,
% 0.98/1.62 c_RealVector_Onorm__class_Onorm [112, 2] (w:1, o:255, a:1, s:1, b:0)
% 0.98/1.62 ,
% 0.98/1.62 v_da____ [113, 0] (w:1, o:64, a:1, s:1, b:0),
% 0.98/1.62 v_aa____ [114, 0] (w:1, o:65, a:1, s:1, b:0),
% 0.98/1.62 c_Rings_Oinverse__class_Odivide [115, 3] (w:1, o:274, a:1, s:1, b:0)
% 0.98/1.62 ,
% 0.98/1.62 v_z____ [116, 0] (w:1, o:66, a:1, s:1, b:0),
% 0.98/1.62 hBOOL [123, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Odivision__ring__inverse__zero [125, 1] (w:1, o:150, a:1
% 0.98/1.62 , s:1, b:0),
% 0.98/1.62 class_Rings_Odivision__ring [126, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.98/1.62 class_Groups_Ouminus [128, 1] (w:1, o:188, a:1, s:1, b:0),
% 0.98/1.62 c_Groups_Otimes__class_Otimes [129, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.98/1.62 class_RealVector_Oreal__normed__vector [130, 1] (w:1, o:152, a:1, s:1
% 0.98/1.62 , b:0),
% 0.98/1.62 class_RealVector_Oreal__normed__field [131, 1] (w:1, o:153, a:1, s:1
% 0.98/1.62 , b:0),
% 0.98/1.62 class_Fields_Olinordered__field__inverse__zero [132, 1] (w:1, o:122
% 0.98/1.62 , a:1, s:1, b:0),
% 0.98/1.62 class_RealVector_Oreal__normed__algebra [133, 1] (w:1, o:154, a:1, s:
% 0.98/1.62 1, b:0),
% 0.98/1.62 class_Fields_Ofield__inverse__zero [134, 1] (w:1, o:123, a:1, s:1, b:
% 0.98/1.62 0),
% 0.98/1.62 class_Lattices_Oab__semigroup__idem__mult [135, 1] (w:1, o:185, a:1
% 0.98/1.62 , s:1, b:0),
% 0.98/1.62 class_RealVector_Oreal__normed__div__algebra [136, 1] (w:1, o:155, a:
% 0.98/1.62 1, s:1, b:0),
% 0.98/1.62 class_Groups_Oab__semigroup__mult [145, 1] (w:1, o:190, a:1, s:1, b:0
% 0.98/1.62 ),
% 0.98/1.62 class_Rings_Omult__zero [146, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Oring__no__zero__divisors [147, 1] (w:1, o:162, a:1, s:1
% 0.98/1.62 , b:0),
% 0.98/1.62 class_Rings_Ono__zero__divisors [148, 1] (w:1, o:163, a:1, s:1, b:0)
% 0.98/1.62 ,
% 0.98/1.62 class_Rings_Osemiring [152, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Ocomm__semiring [153, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Oring [154, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Oidom [155, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.98/1.62 class_Fields_Ofield [156, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Olinordered__ring [157, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Olinordered__ring__strict [158, 1] (w:1, o:147, a:1, s:1
% 0.98/1.62 , b:0),
% 0.98/1.62 class_Rings_Oordered__cancel__semiring [159, 1] (w:1, o:169, a:1, s:1
% 0.98/1.62 , b:0),
% 0.98/1.62 class_Rings_Oordered__ring [160, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Oordered__semiring [161, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.98/1.62
% 0.98/1.62 class_Rings_Oordered__comm__semiring [162, 1] (w:1, o:173, a:1, s:1
% 0.98/1.62 , b:0),
% 0.98/1.62 class_Fields_Olinordered__field [163, 1] (w:1, o:125, a:1, s:1, b:0)
% 0.98/1.62 ,
% 0.98/1.62 class_Rings_Olinordered__semiring__strict [164, 1] (w:1, o:156, a:1
% 0.98/1.62 , s:1, b:0),
% 0.98/1.62 class_Rings_Olinordered__comm__semiring__strict [165, 1] (w:1, o:157
% 0.98/1.62 , a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Olinordered__semiring [166, 1] (w:1, o:158, a:1, s:1, b:0
% 0.98/1.62 ),
% 0.98/1.62 class_Rings_Oordered__ring__abs [167, 1] (w:1, o:171, a:1, s:1, b:0)
% 0.98/1.62 ,
% 0.98/1.62 c_Polynomial_Opoly [170, 2] (w:1, o:256, a:1, s:1, b:0),
% 0.98/1.62 class_Int_Oring__char__0 [174, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Ocomm__semiring__0 [175, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.98/1.62
% 0.98/1.62 class_Rings_Ocomm__ring [177, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.98/1.62 c_Polynomial_Opcompose [180, 3] (w:1, o:275, a:1, s:1, b:0),
% 0.98/1.62 c_Polynomial_Oorder [181, 3] (w:1, o:272, a:1, s:1, b:0),
% 0.98/1.62 c_Complex_Oexpi [186, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.98/1.62 class_Rings_Olinordered__semiring__1__strict [188, 1] (w:1, o:159, a:
% 0.98/1.62 1, s:1, b:0),
% 0.98/1.62 c_Groups_Oone__class_Oone [189, 1] (w:1, o:193, a:1, s:1, b:0),
% 1.26/1.62 c_Complex_Orcis [192, 2] (w:1, o:257, a:1, s:1, b:0),
% 1.26/1.62 class_RealVector_Oreal__normed__algebra__1 [193, 1] (w:1, o:174, a:1
% 1.26/1.62 , s:1, b:0),
% 1.26/1.62 class_Rings_Ozero__neq__one [194, 1] (w:1, o:175, a:1, s:1, b:0),
% 1.26/1.62 class_Groups_Oone [195, 1] (w:1, o:194, a:1, s:1, b:0),
% 1.26/1.62 class_Groups_Ocomm__monoid__mult [196, 1] (w:1, o:195, a:1, s:1, b:0)
% 1.26/1.62 ,
% 1.26/1.62 class_Groups_Omonoid__mult [197, 1] (w:1, o:196, a:1, s:1, b:0),
% 1.26/1.62 class_Rings_Ocomm__ring__1 [198, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.26/1.62 class_Rings_Oring__1__no__zero__divisors [199, 1] (w:1, o:165, a:1
% 1.26/1.62 , s:1, b:0),
% 1.26/1.62 class_Rings_Olinordered__semiring__1 [200, 1] (w:1, o:160, a:1, s:1
% 1.26/1.62 , b:0),
% 1.26/1.62 c_Polynomial_Osynthetic__div [201, 3] (w:1, o:276, a:1, s:1, b:0),
% 1.26/1.62 c_Rings_Odvd__class_Odvd [202, 3] (w:1, o:277, a:1, s:1, b:0),
% 1.26/1.62 class_Rings_Odvd [203, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.26/1.62 class_Rings_Osemiring__0 [204, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.26/1.62 c_Groups_Osgn__class_Osgn [205, 2] (w:1, o:258, a:1, s:1, b:0),
% 1.26/1.62 c_Power_Opower__class_Opower [206, 1] (w:1, o:197, a:1, s:1, b:0),
% 1.26/1.62 class_Groups_Osgn__if [207, 1] (w:1, o:198, a:1, s:1, b:0),
% 1.26/1.62 tc_Int_Oint [208, 0] (w:1, o:96, a:1, s:1, b:0),
% 1.26/1.62 class_Power_Opower [209, 1] (w:1, o:199, a:1, s:1, b:0),
% 1.26/1.62 class_Rings_Oring__1 [210, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.26/1.62 c_Nat_OSuc [212, 1] (w:1, o:200, a:1, s:1, b:0),
% 1.26/1.62 c_Power_Opower_Opower [223, 3] (w:1, o:278, a:1, s:1, b:0),
% 1.26/1.62 c_Groups_Ominus__class_Ominus [228, 3] (w:1, o:279, a:1, s:1, b:0),
% 1.26/1.62 class_Groups_Ominus [230, 1] (w:1, o:201, a:1, s:1, b:0),
% 1.26/1.62 class_RealVector_Oreal__field [234, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.26/1.62 class_Groups_Ocancel__comm__monoid__add [240, 1] (w:1, o:202, a:1, s:
% 1.26/1.62 1, b:0),
% 1.26/1.62 tc_HOL_Obool [242, 0] (w:1, o:95, a:1, s:1, b:0),
% 1.26/1.62 v_mzh [243, 0] (w:1, o:108, a:1, s:1, b:0),
% 1.26/1.62 v_mazh [244, 0] (w:1, o:109, a:1, s:1, b:0),
% 1.26/1.62 v_ma [245, 0] (w:1, o:110, a:1, s:1, b:0),
% 1.26/1.62 alpha1 [246, 3] (w:1, o:280, a:1, s:1, b:1),
% 3.30/3.72 alpha2 [247, 2] (w:1, o:262, a:1, s:1, b:1),
% 3.30/3.72 alpha3 [248, 3] (w:1, o:285, a:1, s:1, b:1),
% 3.30/3.72 alpha4 [249, 3] (w:1, o:290, a:1, s:1, b:1),
% 3.30/3.72 alpha5 [250, 3] (w:1, o:293, a:1, s:1, b:1),
% 3.30/3.72 alpha6 [251, 3] (w:1, o:296, a:1, s:1, b:1),
% 3.30/3.72 alpha7 [252, 3] (w:1, o:297, a:1, s:1, b:1),
% 3.30/3.72 alpha8 [253, 3] (w:1, o:298, a:1, s:1, b:1),
% 3.30/3.72 alpha9 [254, 4] (w:1, o:312, a:1, s:1, b:1),
% 3.30/3.72 alpha10 [255, 4] (w:1, o:313, a:1, s:1, b:1),
% 3.30/3.72 alpha11 [256, 3] (w:1, o:299, a:1, s:1, b:1),
% 3.30/3.72 alpha12 [257, 3] (w:1, o:300, a:1, s:1, b:1),
% 3.30/3.72 alpha13 [258, 3] (w:1, o:301, a:1, s:1, b:1),
% 3.30/3.72 alpha14 [259, 3] (w:1, o:302, a:1, s:1, b:1),
% 3.30/3.72 alpha15 [260, 3] (w:1, o:303, a:1, s:1, b:1),
% 3.30/3.72 alpha16 [261, 3] (w:1, o:304, a:1, s:1, b:1),
% 3.30/3.72 alpha17 [262, 2] (w:1, o:259, a:1, s:1, b:1),
% 3.30/3.72 alpha18 [263, 2] (w:1, o:260, a:1, s:1, b:1),
% 3.30/3.72 alpha19 [264, 2] (w:1, o:261, a:1, s:1, b:1),
% 3.30/3.72 alpha20 [265, 2] (w:1, o:263, a:1, s:1, b:1),
% 3.30/3.72 alpha21 [266, 2] (w:1, o:264, a:1, s:1, b:1),
% 3.30/3.72 alpha22 [267, 3] (w:1, o:281, a:1, s:1, b:1),
% 3.30/3.72 alpha23 [268, 3] (w:1, o:282, a:1, s:1, b:1),
% 3.30/3.72 alpha24 [269, 2] (w:1, o:265, a:1, s:1, b:1),
% 3.30/3.72 alpha25 [270, 4] (w:1, o:314, a:1, s:1, b:1),
% 3.30/3.72 alpha26 [271, 4] (w:1, o:315, a:1, s:1, b:1),
% 3.30/3.72 alpha27 [272, 3] (w:1, o:283, a:1, s:1, b:1),
% 3.30/3.72 alpha28 [273, 3] (w:1, o:284, a:1, s:1, b:1),
% 3.30/3.72 alpha29 [274, 4] (w:1, o:316, a:1, s:1, b:1),
% 3.30/3.72 alpha30 [275, 4] (w:1, o:317, a:1, s:1, b:1),
% 3.30/3.72 alpha31 [276, 4] (w:1, o:318, a:1, s:1, b:1),
% 3.30/3.72 alpha32 [277, 4] (w:1, o:319, a:1, s:1, b:1),
% 3.30/3.72 alpha33 [278, 4] (w:1, o:320, a:1, s:1, b:1),
% 3.30/3.72 alpha34 [279, 4] (w:1, o:321, a:1, s:1, b:1),
% 3.30/3.72 alpha35 [280, 3] (w:1, o:286, a:1, s:1, b:1),
% 3.30/3.72 alpha36 [281, 3] (w:1, o:287, a:1, s:1, b:1),
% 3.30/3.72 alpha37 [282, 3] (w:1, o:288, a:1, s:1, b:1),
% 3.30/3.72 alpha38 [283, 3] (w:1, o:289, a:1, s:1, b:1),
% 3.30/3.72 alpha39 [284, 2] (w:1, o:266, a:1, s:1, b:1),
% 3.30/3.72 alpha40 [285, 2] (w:1, o:267, a:1, s:1, b:1),
% 3.30/3.72 alpha41 [286, 3] (w:1, o:291, a:1, s:1, b:1),
% 3.30/3.72 alpha42 [287, 3] (w:1, o:292, a:1, s:1, b:1),
% 3.30/3.72 alpha43 [288, 4] (w:1, o:322, a:1, s:1, b:1),
% 3.30/3.72 alpha44 [289, 4] (w:1, o:323, a:1, s:1, b:1),
% 3.30/3.72 alpha45 [290, 4] (w:1, o:324, a:1, s:1, b:1),
% 3.30/3.72 alpha46 [291, 4] (w:1, o:325, a:1, s:1, b:1),
% 3.30/3.72 alpha47 [292, 4] (w:1, o:326, a:1, s:1, b:1),
% 3.30/3.72 alpha48 [293, 4] (w:1, o:327, a:1, s:1, b:1),
% 3.30/3.72 alpha49 [294, 4] (w:1, o:328, a:1, s:1, b:1),
% 3.30/3.72 alpha50 [295, 4] (w:1, o:329, a:1, s:1, b:1),
% 3.30/3.72 alpha51 [296, 4] (w:1, o:330, a:1, s:1, b:1),
% 3.30/3.72 alpha52 [297, 4] (w:1, o:331, a:1, s:1, b:1),
% 3.30/3.72 alpha53 [298, 4] (w:1, o:332, a:1, s:1, b:1),
% 3.30/3.72 alpha54 [299, 4] (w:1, o:333, a:1, s:1, b:1),
% 3.30/3.72 alpha55 [300, 3] (w:1, o:294, a:1, s:1, b:1),
% 3.30/3.72 alpha56 [301, 2] (w:1, o:268, a:1, s:1, b:1),
% 3.30/3.72 alpha57 [302, 3] (w:1, o:295, a:1, s:1, b:1),
% 3.30/3.72 skol1 [303, 2] (w:1, o:230, a:1, s:1, b:1),
% 3.30/3.72 skol2 [304, 3] (w:1, o:305, a:1, s:1, b:1),
% 3.30/3.73 skol3 [305, 2] (w:1, o:238, a:1, s:1, b:1),
% 3.30/3.73 skol4 [306, 0] (w:1, o:12, a:1, s:1, b:1),
% 3.30/3.73 skol5 [307, 2] (w:1, o:239, a:1, s:1, b:1),
% 3.30/3.73 skol6 [308, 2] (w:1, o:240, a:1, s:1, b:1),
% 3.30/3.73 skol7 [309, 2] (w:1, o:241, a:1, s:1, b:1),
% 3.30/3.73 skol8 [310, 1] (w:1, o:116, a:1, s:1, b:1),
% 3.30/3.73 skol9 [311, 2] (w:1, o:242, a:1, s:1, b:1),
% 3.30/3.73 skol10 [312, 2] (w:1, o:243, a:1, s:1, b:1),
% 3.30/3.73 skol11 [313, 2] (w:1, o:244, a:1, s:1, b:1),
% 3.30/3.73 skol12 [314, 2] (w:1, o:245, a:1, s:1, b:1),
% 3.30/3.73 skol13 [315, 1] (w:1, o:117, a:1, s:1, b:1),
% 3.30/3.73 skol14 [316, 2] (w:1, o:246, a:1, s:1, b:1),
% 3.30/3.73 skol15 [317, 2] (w:1, o:247, a:1, s:1, b:1),
% 3.30/3.73 skol16 [318, 2] (w:1, o:248, a:1, s:1, b:1),
% 3.30/3.73 skol17 [319, 2] (w:1, o:249, a:1, s:1, b:1),
% 3.30/3.73 skol18 [320, 1] (w:1, o:118, a:1, s:1, b:1),
% 3.30/3.73 skol19 [321, 2] (w:1, o:250, a:1, s:1, b:1),
% 3.30/3.73 skol20 [322, 3] (w:1, o:306, a:1, s:1, b:1),
% 3.30/3.73 skol21 [323, 3] (w:1, o:307, a:1, s:1, b:1),
% 3.30/3.73 skol22 [324, 2] (w:1, o:231, a:1, s:1, b:1),
% 23.12/23.50 skol23 [325, 1] (w:1, o:119, a:1, s:1, b:1),
% 23.12/23.50 skol24 [326, 2] (w:1, o:232, a:1, s:1, b:1),
% 23.12/23.50 skol25 [327, 2] (w:1, o:233, a:1, s:1, b:1),
% 23.12/23.50 skol26 [328, 2] (w:1, o:234, a:1, s:1, b:1),
% 23.12/23.50 skol27 [329, 2] (w:1, o:235, a:1, s:1, b:1),
% 23.12/23.50 skol28 [330, 2] (w:1, o:236, a:1, s:1, b:1),
% 23.12/23.50 skol29 [331, 2] (w:1, o:237, a:1, s:1, b:1),
% 23.12/23.50 skol30 [332, 3] (w:1, o:308, a:1, s:1, b:1),
% 23.12/23.50 skol31 [333, 3] (w:1, o:309, a:1, s:1, b:1),
% 23.12/23.50 skol32 [334, 3] (w:1, o:310, a:1, s:1, b:1).
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Starting Search:
% 23.12/23.50
% 23.12/23.50 *** allocated 113905 integers for clauses
% 23.12/23.50 *** allocated 170857 integers for clauses
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 2786
% 23.12/23.50 Kept: 2001
% 23.12/23.50 Inuse: 21
% 23.12/23.50 Deleted: 1
% 23.12/23.50 Deletedinuse: 0
% 23.12/23.50
% 23.12/23.50 *** allocated 256285 integers for clauses
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 *** allocated 170857 integers for termspace/termends
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 7706
% 23.12/23.50 Kept: 4261
% 23.12/23.50 Inuse: 190
% 23.12/23.50 Deleted: 1
% 23.12/23.50 Deletedinuse: 0
% 23.12/23.50
% 23.12/23.50 *** allocated 384427 integers for clauses
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 *** allocated 256285 integers for termspace/termends
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 13469
% 23.12/23.50 Kept: 6466
% 23.12/23.50 Inuse: 273
% 23.12/23.50 Deleted: 3
% 23.12/23.50 Deletedinuse: 0
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 *** allocated 576640 integers for clauses
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 19358
% 23.12/23.50 Kept: 8568
% 23.12/23.50 Inuse: 318
% 23.12/23.50 Deleted: 3
% 23.12/23.50 Deletedinuse: 0
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 *** allocated 384427 integers for termspace/termends
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 24426
% 23.12/23.50 Kept: 10625
% 23.12/23.50 Inuse: 377
% 23.12/23.50 Deleted: 4
% 23.12/23.50 Deletedinuse: 0
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 *** allocated 864960 integers for clauses
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 29720
% 23.12/23.50 Kept: 12650
% 23.12/23.50 Inuse: 423
% 23.12/23.50 Deleted: 7
% 23.12/23.50 Deletedinuse: 0
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 35175
% 23.12/23.50 Kept: 14677
% 23.12/23.50 Inuse: 466
% 23.12/23.50 Deleted: 7
% 23.12/23.50 Deletedinuse: 0
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 *** allocated 576640 integers for termspace/termends
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 40641
% 23.12/23.50 Kept: 16690
% 23.12/23.50 Inuse: 506
% 23.12/23.50 Deleted: 7
% 23.12/23.50 Deletedinuse: 0
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 *** allocated 1297440 integers for clauses
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 46154
% 23.12/23.50 Kept: 18709
% 23.12/23.50 Inuse: 535
% 23.12/23.50 Deleted: 8
% 23.12/23.50 Deletedinuse: 0
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 Resimplifying clauses:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 50829
% 23.12/23.50 Kept: 20721
% 23.12/23.50 Inuse: 556
% 23.12/23.50 Deleted: 264
% 23.12/23.50 Deletedinuse: 0
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 56425
% 23.12/23.50 Kept: 22756
% 23.12/23.50 Inuse: 598
% 23.12/23.50 Deleted: 265
% 23.12/23.50 Deletedinuse: 1
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 61795
% 23.12/23.50 Kept: 25445
% 23.12/23.50 Inuse: 633
% 23.12/23.50 Deleted: 265
% 23.12/23.50 Deletedinuse: 1
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 *** allocated 864960 integers for termspace/termends
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 65448
% 23.12/23.50 Kept: 27517
% 23.12/23.50 Inuse: 653
% 23.12/23.50 Deleted: 265
% 23.12/23.50 Deletedinuse: 1
% 23.12/23.50
% 23.12/23.50 *** allocated 1946160 integers for clauses
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 70211
% 23.12/23.50 Kept: 29601
% 23.12/23.50 Inuse: 693
% 23.12/23.50 Deleted: 265
% 23.12/23.50 Deletedinuse: 1
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 75884
% 23.12/23.50 Kept: 32976
% 23.12/23.50 Inuse: 718
% 23.12/23.50 Deleted: 265
% 23.12/23.50 Deletedinuse: 1
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 79336
% 23.12/23.50 Kept: 35366
% 23.12/23.50 Inuse: 723
% 23.12/23.50 Deleted: 265
% 23.12/23.50 Deletedinuse: 1
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 83881
% 23.12/23.50 Kept: 37453
% 23.12/23.50 Inuse: 763
% 23.12/23.50 Deleted: 265
% 23.12/23.50 Deletedinuse: 1
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50
% 23.12/23.50 Intermediate Status:
% 23.12/23.50 Generated: 88219
% 23.12/23.50 Kept: 39458
% 23.12/23.50 Inuse: 793
% 23.12/23.50 Deleted: 265
% 23.12/23.50 Deletedinuse: 1
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 23.12/23.50 Done
% 23.12/23.50
% 23.12/23.50 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying clauses:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 91309
% 84.82/85.29 Kept: 41492
% 84.82/85.29 Inuse: 805
% 84.82/85.29 Deleted: 429
% 84.82/85.29 Deletedinuse: 1
% 84.82/85.29
% 84.82/85.29 *** allocated 1297440 integers for termspace/termends
% 84.82/85.29 *** allocated 2919240 integers for clauses
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 95918
% 84.82/85.29 Kept: 44850
% 84.82/85.29 Inuse: 813
% 84.82/85.29 Deleted: 429
% 84.82/85.29 Deletedinuse: 1
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 100930
% 84.82/85.29 Kept: 48343
% 84.82/85.29 Inuse: 823
% 84.82/85.29 Deleted: 429
% 84.82/85.29 Deletedinuse: 1
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 105858
% 84.82/85.29 Kept: 50438
% 84.82/85.29 Inuse: 848
% 84.82/85.29 Deleted: 429
% 84.82/85.29 Deletedinuse: 1
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 109153
% 84.82/85.29 Kept: 52478
% 84.82/85.29 Inuse: 856
% 84.82/85.29 Deleted: 430
% 84.82/85.29 Deletedinuse: 2
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 114235
% 84.82/85.29 Kept: 54522
% 84.82/85.29 Inuse: 869
% 84.82/85.29 Deleted: 430
% 84.82/85.29 Deletedinuse: 2
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 119768
% 84.82/85.29 Kept: 56575
% 84.82/85.29 Inuse: 896
% 84.82/85.29 Deleted: 430
% 84.82/85.29 Deletedinuse: 2
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 125300
% 84.82/85.29 Kept: 59395
% 84.82/85.29 Inuse: 913
% 84.82/85.29 Deleted: 430
% 84.82/85.29 Deletedinuse: 2
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 130261
% 84.82/85.29 Kept: 61854
% 84.82/85.29 Inuse: 928
% 84.82/85.29 Deleted: 430
% 84.82/85.29 Deletedinuse: 2
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying clauses:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 135992
% 84.82/85.29 Kept: 63888
% 84.82/85.29 Inuse: 954
% 84.82/85.29 Deleted: 488
% 84.82/85.29 Deletedinuse: 2
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 *** allocated 1946160 integers for termspace/termends
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 142107
% 84.82/85.29 Kept: 65934
% 84.82/85.29 Inuse: 980
% 84.82/85.29 Deleted: 488
% 84.82/85.29 Deletedinuse: 2
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 *** allocated 4378860 integers for clauses
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 147410
% 84.82/85.29 Kept: 67990
% 84.82/85.29 Inuse: 1003
% 84.82/85.29 Deleted: 488
% 84.82/85.29 Deletedinuse: 2
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 151896
% 84.82/85.29 Kept: 70896
% 84.82/85.29 Inuse: 1013
% 84.82/85.29 Deleted: 488
% 84.82/85.29 Deletedinuse: 2
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 158211
% 84.82/85.29 Kept: 72949
% 84.82/85.29 Inuse: 1038
% 84.82/85.29 Deleted: 488
% 84.82/85.29 Deletedinuse: 2
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 168889
% 84.82/85.29 Kept: 76107
% 84.82/85.29 Inuse: 1054
% 84.82/85.29 Deleted: 488
% 84.82/85.29 Deletedinuse: 2
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 174407
% 84.82/85.29 Kept: 78112
% 84.82/85.29 Inuse: 1088
% 84.82/85.29 Deleted: 489
% 84.82/85.29 Deletedinuse: 3
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 181624
% 84.82/85.29 Kept: 82079
% 84.82/85.29 Inuse: 1123
% 84.82/85.29 Deleted: 489
% 84.82/85.29 Deletedinuse: 3
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying clauses:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 187128
% 84.82/85.29 Kept: 84079
% 84.82/85.29 Inuse: 1155
% 84.82/85.29 Deleted: 1527
% 84.82/85.29 Deletedinuse: 3
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 196156
% 84.82/85.29 Kept: 89453
% 84.82/85.29 Inuse: 1178
% 84.82/85.29 Deleted: 1527
% 84.82/85.29 Deletedinuse: 3
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 203779
% 84.82/85.29 Kept: 91513
% 84.82/85.29 Inuse: 1218
% 84.82/85.29 Deleted: 1527
% 84.82/85.29 Deletedinuse: 3
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 213630
% 84.82/85.29 Kept: 94240
% 84.82/85.29 Inuse: 1228
% 84.82/85.29 Deleted: 1527
% 84.82/85.29 Deletedinuse: 3
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 220876
% 84.82/85.29 Kept: 99288
% 84.82/85.29 Inuse: 1238
% 84.82/85.29 Deleted: 1527
% 84.82/85.29 Deletedinuse: 3
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 *** allocated 6568290 integers for clauses
% 84.82/85.29 *** allocated 2919240 integers for termspace/termends
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 84.82/85.29 Generated: 236418
% 84.82/85.29 Kept: 103671
% 84.82/85.29 Inuse: 1283
% 84.82/85.29 Deleted: 1527
% 84.82/85.29 Deletedinuse: 3
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying clauses:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29 Resimplifying inuse:
% 84.82/85.29 Done
% 84.82/85.29
% 84.82/85.29
% 84.82/85.29 Intermediate Status:
% 259.52/260.01 Generated: 244308
% 259.52/260.01 Kept: 105684
% 259.52/260.01 Inuse: 1324
% 259.52/260.01 Deleted: 1640
% 259.52/260.01 Deletedinuse: 3
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 252712
% 259.52/260.01 Kept: 108350
% 259.52/260.01 Inuse: 1361
% 259.52/260.01 Deleted: 1643
% 259.52/260.01 Deletedinuse: 4
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 259592
% 259.52/260.01 Kept: 110352
% 259.52/260.01 Inuse: 1399
% 259.52/260.01 Deleted: 1646
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 268878
% 259.52/260.01 Kept: 112778
% 259.52/260.01 Inuse: 1424
% 259.52/260.01 Deleted: 1646
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 283575
% 259.52/260.01 Kept: 116592
% 259.52/260.01 Inuse: 1444
% 259.52/260.01 Deleted: 1646
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 288795
% 259.52/260.01 Kept: 119795
% 259.52/260.01 Inuse: 1449
% 259.52/260.01 Deleted: 1646
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 293393
% 259.52/260.01 Kept: 123052
% 259.52/260.01 Inuse: 1454
% 259.52/260.01 Deleted: 1646
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying clauses:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 299324
% 259.52/260.01 Kept: 126770
% 259.52/260.01 Inuse: 1464
% 259.52/260.01 Deleted: 1909
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 304154
% 259.52/260.01 Kept: 130073
% 259.52/260.01 Inuse: 1469
% 259.52/260.01 Deleted: 1909
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 309001
% 259.52/260.01 Kept: 133345
% 259.52/260.01 Inuse: 1474
% 259.52/260.01 Deleted: 1909
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 322444
% 259.52/260.01 Kept: 137595
% 259.52/260.01 Inuse: 1489
% 259.52/260.01 Deleted: 1909
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 328042
% 259.52/260.01 Kept: 139721
% 259.52/260.01 Inuse: 1509
% 259.52/260.01 Deleted: 1909
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 337120
% 259.52/260.01 Kept: 142347
% 259.52/260.01 Inuse: 1524
% 259.52/260.01 Deleted: 1909
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 342537
% 259.52/260.01 Kept: 145789
% 259.52/260.01 Inuse: 1529
% 259.52/260.01 Deleted: 1909
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying clauses:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 348017
% 259.52/260.01 Kept: 149236
% 259.52/260.01 Inuse: 1534
% 259.52/260.01 Deleted: 2035
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 354985
% 259.52/260.01 Kept: 151360
% 259.52/260.01 Inuse: 1554
% 259.52/260.01 Deleted: 2035
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 *** allocated 4378860 integers for termspace/termends
% 259.52/260.01 *** allocated 9852435 integers for clauses
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 370054
% 259.52/260.01 Kept: 155706
% 259.52/260.01 Inuse: 1569
% 259.52/260.01 Deleted: 2035
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 384387
% 259.52/260.01 Kept: 159628
% 259.52/260.01 Inuse: 1579
% 259.52/260.01 Deleted: 2035
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 393692
% 259.52/260.01 Kept: 161798
% 259.52/260.01 Inuse: 1604
% 259.52/260.01 Deleted: 2035
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 400181
% 259.52/260.01 Kept: 163918
% 259.52/260.01 Inuse: 1624
% 259.52/260.01 Deleted: 2035
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 407825
% 259.52/260.01 Kept: 165934
% 259.52/260.01 Inuse: 1649
% 259.52/260.01 Deleted: 2035
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying clauses:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 416051
% 259.52/260.01 Kept: 167977
% 259.52/260.01 Inuse: 1674
% 259.52/260.01 Deleted: 2079
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 435238
% 259.52/260.01 Kept: 171695
% 259.52/260.01 Inuse: 1689
% 259.52/260.01 Deleted: 2079
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 456001
% 259.52/260.01 Kept: 175537
% 259.52/260.01 Inuse: 1704
% 259.52/260.01 Deleted: 2079
% 259.52/260.01 Deletedinuse: 5
% 259.52/260.01
% 259.52/260.01 Resimplifying inuse:
% 259.52/260.01 Done
% 259.52/260.01
% 259.52/260.01
% 259.52/260.01 Intermediate Status:
% 259.52/260.01 Generated: 490884
% 259.52/260.01 Kept: 179301
% 259.52/260.01 ICputime limit exceeded (core dumped)
%------------------------------------------------------------------------------