TSTP Solution File: SWW178+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW178+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 23:21:03 EDT 2022
% Result : Timeout 300.09s 300.61s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW178+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sat Jun 4 15:08:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.89/1.50 *** allocated 10000 integers for termspace/termends
% 0.89/1.50 *** allocated 10000 integers for clauses
% 0.89/1.50 *** allocated 10000 integers for justifications
% 0.89/1.50 *** allocated 15000 integers for termspace/termends
% 0.89/1.50 *** allocated 22500 integers for termspace/termends
% 0.89/1.50 *** allocated 33750 integers for termspace/termends
% 0.89/1.50 Bliksem 1.12
% 0.89/1.50
% 0.89/1.50
% 0.89/1.50 Automatic Strategy Selection
% 0.89/1.50
% 0.89/1.50 *** allocated 50625 integers for termspace/termends
% 0.89/1.50 *** allocated 75937 integers for termspace/termends
% 0.89/1.50 *** allocated 113905 integers for termspace/termends
% 0.89/1.50
% 0.89/1.50 Clauses:
% 0.89/1.50
% 0.89/1.50 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.89/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_w, v_z ),
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_z ) ) ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_w, v_z ) ) ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_z ) ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.89/1.50 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.50 ( X, Y ) ) ) }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.89/1.50 , Y ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.50 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.50 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.50 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.50 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.89/1.50 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.50 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.89/1.50 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.89/1.50 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.50 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.89/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.89/1.50 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.89/1.50 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.89/1.50 X, Z, Y ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.89/1.50 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.89/1.50 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.89/1.50 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.89/1.50 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.89/1.50 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.89/1.50 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.89/1.50 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 Z, Y ) ) = Y }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.89/1.50 Y ) ) = Y }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.89/1.50 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.89/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.89/1.50 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.89/1.50 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.89/1.50 ( X, Y, Z ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.89/1.50 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.50 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.50 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.89/1.50 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.50 ( X, Y ) ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.89/1.50 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.89/1.50 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.89/1.50 ( X, T, Y ) ) ) ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.89/1.50 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.89/1.50 hAPP( Y, U ) ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.50 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.89/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.89/1.50 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.89/1.50 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.50 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.89/1.50 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.89/1.50 hAPP( Y, U ) ) }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.89/1.50 ( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.89/1.50 ( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.89/1.50 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.89/1.50 hAPP( Y, U ) ) }.
% 0.89/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.89/1.50 ( Z, skol2( X, Y, Z ) ), hAPP( Y, skol2( X, Y, Z ) ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.89/1.50 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 Y, T ), Z = Y }.
% 0.89/1.50 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 T, Y ), Z = Y }.
% 0.89/1.50 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 T, Y ), Z = Y }.
% 0.89/1.50 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 Y, Z ), T = Y }.
% 0.89/1.50 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 Y, Z ) }.
% 0.89/1.50 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 T, Y ), Z = Y }.
% 0.89/1.50 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 T, Y ) }.
% 0.89/1.50 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.89/1.50 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.89/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.89/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.89/1.50 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.89/1.50 X, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.89/1.50 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.89/1.50 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.89/1.50 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.89/1.50 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.50 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.50 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.89/1.50 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.89/1.50 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.89/1.50 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.89/1.50 ) ) }.
% 0.89/1.50 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, Y ), Z = Y }.
% 0.89/1.50 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, Y ) }.
% 0.89/1.50 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.89/1.50 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.89/1.50 hAPP( Z, Y ) ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.89/1.50 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.89/1.50 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.89/1.50 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ) }.
% 0.89/1.50 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.89/1.50 ( tc_RealDef_Oreal, Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.89/1.50 , X ) ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ) }.
% 0.89/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.89/1.50 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z )
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) ) ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.89/1.50 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.89/1.50 ( tc_RealDef_Oreal, Z, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.89/1.50 , X ) ) ) ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.89/1.50 ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.89/1.50 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.89/1.50 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.89/1.50 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.89/1.50 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.89/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.89/1.50 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.50 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.89/1.50 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.89/1.50 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.89/1.50 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.50 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.89/1.50 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.89/1.50 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.89/1.50 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.89/1.50 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.89/1.50 Y ) ) ) ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.89/1.50 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.89/1.50 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.89/1.50 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.89/1.50 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.89/1.50 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.89/1.50 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Orcis( Y
% 0.89/1.50 , X ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 ), c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.89/1.50 X, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , c_Groups_Oabs__class_Oabs( X, Y ) ), c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.50 }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.89/1.50 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.89/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Complex_OIm( X ) ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.89/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Complex_ORe( X ) ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, c_RealVector_OscaleR__class_OscaleR( X
% 0.89/1.50 , U, T ), c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) =
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Ominus__class_Ominus(
% 0.89/1.50 tc_RealDef_Oreal, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Ominus__class_Ominus(
% 0.89/1.50 tc_RealDef_Oreal, U, Z ), Y ) ), c_RealVector_OscaleR__class_OscaleR( X,
% 0.89/1.50 Z, c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.89/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.89/1.50 ( Z, skol3( X, Y, Z ) ), hAPP( Y, skol3( X, Y, Z ) ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_RealVector_Obounded__bilinear( Z, X, Y, T ),
% 0.89/1.50 c_Groups_Ominus__class_Ominus( Y, hAPP( hAPP( T, V1 ), V0 ), hAPP( hAPP(
% 0.89/1.50 T, W ), U ) ) = c_Groups_Oplus__class_Oplus( Y,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( Y, hAPP( hAPP( T,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( Z, V1, W ) ),
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, V0, U ) ), hAPP( hAPP( T,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( Z, V1, W ) ), U ) ), hAPP( hAPP( T, W ),
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, V0, U ) ) ) }.
% 0.89/1.50 { c_RealVector_Odist__class_Odist( tc_RealDef_Oreal, Y, X ) =
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.89/1.50 { ! c_Complex_ORe( Y ) = c_Complex_ORe( X ), ! c_Complex_OIm( Y ) =
% 0.89/1.50 c_Complex_OIm( X ), Y = X }.
% 0.89/1.50 { ! Y = X, c_Complex_ORe( Y ) = c_Complex_ORe( X ) }.
% 0.89/1.50 { ! Y = X, c_Complex_OIm( Y ) = c_Complex_OIm( X ) }.
% 0.89/1.50 { ! c_Complex_ORe( Y ) = c_Complex_ORe( X ), ! c_Complex_OIm( Y ) =
% 0.89/1.50 c_Complex_OIm( X ), Y = X }.
% 0.89/1.50 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.89/1.50 { c_Complex_ORe( c_RealVector_OscaleR__class_OscaleR( tc_Complex_Ocomplex,
% 0.89/1.50 Y, X ) ) = c_RealVector_OscaleR__class_OscaleR( tc_RealDef_Oreal, Y,
% 0.89/1.50 c_Complex_ORe( X ) ) }.
% 0.89/1.50 { c_Complex_OIm( c_RealVector_OscaleR__class_OscaleR( tc_Complex_Ocomplex,
% 0.89/1.50 Y, X ) ) = c_RealVector_OscaleR__class_OscaleR( tc_RealDef_Oreal, Y,
% 0.89/1.50 c_Complex_OIm( X ) ) }.
% 0.89/1.50 { c_Complex_ORe( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.50 { c_Complex_OIm( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.50 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.50 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.89/1.50 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.50 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.50 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.89/1.50 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.89/1.50 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.89/1.50 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.89/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.50 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.50 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.50 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.50 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.50 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.89/1.50 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.89/1.50 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.89/1.50 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.50 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.50 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.50 , ! Y = Z }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.50 , ! Z = Y }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.50 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.50 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.50 , ! Z = Y }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.50 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.50 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ), ! c_RealVector_OscaleR__class_OscaleR( X, T, Y ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ), T = Z }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_RealDef_Oreal ), ! c_RealVector_OscaleR__class_OscaleR( X, Y, T ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Y, Z ), T = Z }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_RealVector_Obounded__bilinear( Z, X, Y, T ), hAPP( hAPP( T,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( Z, V0, W ) ), U ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( Y, V0, hAPP( hAPP( T, W ), U ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_RealVector_Obounded__bilinear( Z, X, Y, T ), hAPP( hAPP( T, V0 ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, W, U ) ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( Y, W, hAPP( hAPP( T, V0 ), U ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_RealVector_Obounded__bilinear( Y, Z, X, T ), hAPP( hAPP( T, U ),
% 0.89/1.50 c_Groups_Ozero__class_Ozero( Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_RealVector_Obounded__bilinear( Y, Z, X, T ), hAPP( hAPP( T,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( Y ) ), U ) = c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ), !
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Z ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Y, Z ), T = Y, Z =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ), ! T = Y,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Z ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Y, Z ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.89/1.50 ( X ), c_RealVector_OscaleR__class_OscaleR( X, T, Z ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Y, Z ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ), !
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Z ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ), Z = Y, T =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ), ! Z = Y,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Z ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ), ! T = c_Groups_Ozero__class_Ozero
% 0.89/1.50 ( tc_RealDef_Oreal ), c_RealVector_OscaleR__class_OscaleR( X, T, Z ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( tc_RealDef_Oreal, T, Z ), Y ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( tc_RealDef_Oreal, T, Z ), Y ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ), !
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.89/1.50 ( tc_RealDef_Oreal ), c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.89/1.50 ( X ), c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_RealVector_Ometric__space( X ), ! c_RealVector_Odist__class_Odist
% 0.89/1.50 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z = Y }.
% 0.89/1.50 { ! class_RealVector_Ometric__space( X ), ! Z = Y,
% 0.89/1.50 c_RealVector_Odist__class_Odist( X, Z, Y ) = c_Groups_Ozero__class_Ozero
% 0.89/1.50 ( tc_RealDef_Oreal ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) =
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ) ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.50 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_RealVector_Ometric__space( X ), c_RealVector_Odist__class_Odist(
% 0.89/1.50 X, Z, Y ) = c_RealVector_Odist__class_Odist( X, Y, Z ) }.
% 0.89/1.50 { ! class_RealVector_Ometric__space( X ), c_RealVector_Odist__class_Odist(
% 0.89/1.50 X, Y, Y ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_RealVector_Ometric__space( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.50 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.50 c_RealVector_Odist__class_Odist( X, Z, Y ) ), ! Z = Y }.
% 0.89/1.50 { ! class_RealVector_Ometric__space( X ), Z = Y,
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.50 c_RealVector_Odist__class_Odist( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.89/1.50 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_RealDef_Oreal ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_RealDef_Oreal ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.50 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.50 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.50 Y ), ! Z = Y }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.50 Z ), ! Z = Y }.
% 0.89/1.50 { ! class_RealVector_Ometric__space( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.50 tc_RealDef_Oreal, c_RealVector_Odist__class_Odist( X, Z, Y ),
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.50 Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.50 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.89/1.50 ( X ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.89/1.50 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , Z, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.89/1.50 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.89/1.50 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.89/1.50 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.89/1.50 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 , Y ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.89/1.50 , Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_RealDef_Oreal ) ) }.
% 0.89/1.50 { ! class_RealVector_Ometric__space( X ), c_Orderings_Oord__class_Oless__eq
% 0.89/1.50 ( tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.50 c_RealVector_Odist__class_Odist( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Ometric__space( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Odist__class_Odist( X, Z, Y ), c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_RealDef_Oreal ) ), Z = Y }.
% 0.89/1.50 { ! class_RealVector_Ometric__space( X ), ! Z = Y,
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Odist__class_Odist( X, Z, Y ), c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_RealDef_Oreal ) ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.89/1.50 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) = c_RealVector_Odist__class_Odist
% 0.89/1.50 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.89/1.50 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.89/1.50 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.89/1.50 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.50 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.89/1.50 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.89/1.50 ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.50 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.89/1.50 ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.50 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.89/1.50 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 0.89/1.50 }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, c_Groups_Oplus__class_Oplus( X
% 0.89/1.50 , Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Z ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, c_Groups_Oplus__class_Oplus( X
% 0.89/1.50 , Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Z ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, c_Groups_Ominus__class_Ominus
% 0.89/1.50 ( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Z ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, c_Groups_Ominus__class_Ominus
% 0.89/1.50 ( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Z ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.50 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.50 X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.50 X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Ouminus__class_Ouminus(
% 0.89/1.50 tc_RealDef_Oreal, Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Ouminus__class_Ouminus(
% 0.89/1.50 tc_RealDef_Oreal, Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Ouminus__class_Ouminus(
% 0.89/1.50 tc_RealDef_Oreal, Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.50 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.50 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.50 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.50 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.50 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.50 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.50 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.50 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.50 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.50 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.50 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.50 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.89/1.50 ( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.50 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.50 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.50 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.50 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.50 , ! Z = Y }.
% 0.89/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.50 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.50 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.50 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.50 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.50 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.50 { c_Complex_ORe( c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X )
% 0.89/1.50 ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_Complex_ORe( Y )
% 0.89/1.50 , c_Complex_ORe( X ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.89/1.50 ( X, Z, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.89/1.50 ( X, Z, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.50 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.89/1.50 , T ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.50 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.50 , T, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.50 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.50 , Y, T ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.89/1.50 ( X, Z, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.50 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.50 , T, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.89/1.50 ( X, T, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.50 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.50 , Y, Z ) ) }.
% 0.89/1.50 { c_Complex_OIm( c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X )
% 0.89/1.50 ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_Complex_OIm( Y )
% 0.89/1.50 , c_Complex_OIm( X ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.89/1.50 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.89/1.50 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.50 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.50 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.89/1.50 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, Y ), Z ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.89/1.50 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, Z ), Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.89/1.50 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.89/1.50 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.50 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.50 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.89/1.50 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.89/1.50 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.89/1.50 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.89/1.50 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.89/1.50 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.89/1.50 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.50 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.50 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.89/1.50 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.89/1.50 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.89/1.50 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.89/1.50 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 = Y }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.89/1.50 ( X ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Y ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.89/1.50 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.89/1.50 = Y }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.89/1.50 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.50 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.89/1.50 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.50 { c_Complex_ORe( c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X )
% 0.89/1.50 ) = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_Complex_ORe( X
% 0.89/1.50 ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_RealVector_Obounded__bilinear( Z, X, Y, T ), hAPP( hAPP( T,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( Z, V0, W ) ), U ) =
% 0.89/1.50 c_Groups_Oplus__class_Oplus( Y, hAPP( hAPP( T, V0 ), U ), hAPP( hAPP( T,
% 0.89/1.50 W ), U ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_RealVector_Obounded__bilinear( Z, X, Y, T ), hAPP( hAPP( T, V0 ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, W, U ) ) = c_Groups_Oplus__class_Oplus( Y
% 0.89/1.50 , hAPP( hAPP( T, V0 ), W ), hAPP( hAPP( T, V0 ), U ) ) }.
% 0.89/1.50 { c_Complex_OIm( c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X )
% 0.89/1.50 ) = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_Complex_OIm( X
% 0.89/1.50 ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_RealVector_Obounded__bilinear( Z, X, Y, T ), hAPP( hAPP( T, V0 ),
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, W, U ) ) =
% 0.89/1.50 c_Groups_Ominus__class_Ominus( Y, hAPP( hAPP( T, V0 ), W ), hAPP( hAPP( T
% 0.89/1.50 , V0 ), U ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_RealVector_Obounded__bilinear( Z, X, Y, T ), hAPP( hAPP( T,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( Z, V0, W ) ), U ) =
% 0.89/1.50 c_Groups_Ominus__class_Ominus( Y, hAPP( hAPP( T, V0 ), U ), hAPP( hAPP( T
% 0.89/1.50 , W ), U ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_RealVector_Obounded__bilinear( Z, X, Y, T ), hAPP( hAPP( T, W ),
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, U ) ) =
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( Y, hAPP( hAPP( T, W ), U ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.50 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.50 c_RealVector_Obounded__bilinear( Z, X, Y, T ), hAPP( hAPP( T,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( Z, W ) ), U ) =
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( Y, hAPP( hAPP( T, W ), U ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Oplus__class_Oplus(
% 0.89/1.50 tc_RealDef_Oreal, T, Z ), Y ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Oplus__class_Oplus(
% 0.89/1.50 tc_RealDef_Oreal, T, Z ), Y ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Oplus__class_Oplus(
% 0.89/1.50 tc_RealDef_Oreal, T, Z ), Y ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Ominus__class_Ominus(
% 0.89/1.50 tc_RealDef_Oreal, T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Ominus__class_Ominus(
% 0.89/1.50 tc_RealDef_Oreal, T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Ominus__class_Ominus(
% 0.89/1.50 tc_RealDef_Oreal, T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, T, Y ),
% 0.89/1.50 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.89/1.50 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.50 , Y, T ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.89/1.50 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Complex_ORe( X ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 Z, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 Y, Z ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.50 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.89/1.50 .
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.50 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.89/1.50 .
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.50 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.89/1.50 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.50 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.89/1.50 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.89/1.50 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.89/1.50 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.89/1.50 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, Y ), Y ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.50 X ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.89/1.50 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, Y ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.89/1.50 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.89/1.50 ( X, Z ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.50 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.89/1.50 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.50 Z ) = Y }.
% 0.89/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.89/1.50 X, Y ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.50 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.50 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.89/1.50 { c_Complex_ORe( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) )
% 0.89/1.50 = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Complex_ORe( Y ),
% 0.89/1.50 c_Complex_ORe( X ) ) }.
% 0.89/1.50 { c_Complex_OIm( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) )
% 0.89/1.50 = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Complex_OIm( Y ),
% 0.89/1.50 c_Complex_OIm( X ) ) }.
% 0.89/1.50 { ! class_RealVector_Odist__norm( X ), c_RealVector_Odist__class_Odist( X,
% 0.89/1.50 Z, Y ) = c_RealVector_Onorm__class_Onorm( X,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.89/1.50 { ! class_RealVector_Ometric__space( X ), c_Orderings_Oord__class_Oless__eq
% 0.89/1.50 ( tc_RealDef_Oreal, c_RealVector_Odist__class_Odist( X, T, Z ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Odist__class_Odist( X, T, Y ),
% 0.89/1.50 c_RealVector_Odist__class_Odist( X, Y, Z ) ) ) }.
% 0.89/1.50 { ! class_RealVector_Ometric__space( X ), c_Orderings_Oord__class_Oless__eq
% 0.89/1.50 ( tc_RealDef_Oreal, c_RealVector_Odist__class_Odist( X, T, Z ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Odist__class_Odist( X, T, Y ),
% 0.89/1.50 c_RealVector_Odist__class_Odist( X, Z, Y ) ) ) }.
% 0.89/1.50 { ! class_RealVector_Ometric__space( X ), c_Orderings_Oord__class_Oless__eq
% 0.89/1.50 ( tc_RealDef_Oreal, c_RealVector_Odist__class_Odist( X, T, Z ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Odist__class_Odist( X, Y, T ),
% 0.89/1.50 c_RealVector_Odist__class_Odist( X, Y, Z ) ) ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.89/1.50 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.89/1.50 ( X, Z, Y ), T ) }.
% 0.89/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.89/1.50 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.89/1.50 ( X, Z, Y ) ) }.
% 0.89/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.89/1.50 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.89/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.50 X, Z, Y ) }.
% 0.89/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.50 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.89/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 0.89/1.50 }.
% 0.89/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.89/1.50 .
% 0.89/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.89/1.50 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.89/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ) ) }.
% 0.89/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.89/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.50 ) ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.50 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.50 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.89/1.50 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol4( T, U, W ) ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol4( X, Y, Z
% 0.89/1.50 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, T ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol4( X, Y, Z
% 0.89/1.50 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, T, Z ) }.
% 0.89/1.50 { c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) =
% 0.89/1.50 c_Complex_Ocomplex_OComplex( c_Groups_Ouminus__class_Ouminus(
% 0.89/1.50 tc_RealDef_Oreal, c_Complex_ORe( X ) ), c_Groups_Ouminus__class_Ouminus(
% 0.89/1.50 tc_RealDef_Oreal, c_Complex_OIm( X ) ) ) }.
% 0.89/1.50 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) =
% 0.89/1.50 c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus(
% 0.89/1.50 tc_RealDef_Oreal, c_Complex_ORe( Y ), c_Complex_ORe( X ) ),
% 0.89/1.50 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Complex_OIm( Y ),
% 0.89/1.50 c_Complex_OIm( X ) ) ) }.
% 0.89/1.50 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.89/1.50 ) }.
% 0.89/1.50 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.89/1.50 ) }.
% 0.89/1.50 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.50 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_Complex_Ocomplex ) }.
% 0.89/1.50 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) =
% 0.89/1.50 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.50 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.89/1.50 ), T = Y }.
% 0.89/1.50 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.89/1.50 ), Z = X }.
% 0.89/1.50 { ! T = Y, ! Z = X, c_Complex_Ocomplex_OComplex( T, Z ) =
% 0.89/1.50 c_Complex_Ocomplex_OComplex( Y, X ) }.
% 0.89/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.89/1.50 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.89/1.50 .
% 0.89/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.89/1.50 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.89/1.50 }.
% 0.89/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.89/1.50 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.89/1.50 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.89/1.50 { c_Complex_ORe( c_Complex_Ocomplex_OComplex( Y, X ) ) = Y }.
% 0.89/1.50 { c_Complex_OIm( c_Complex_Ocomplex_OComplex( Y, X ) ) = X }.
% 0.89/1.50 { c_Complex_Ocomplex_OComplex( c_Complex_ORe( X ), c_Complex_OIm( X ) ) = X
% 0.89/1.50 }.
% 0.89/1.50 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.89/1.50 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.89/1.50 ) = c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus(
% 0.89/1.50 tc_RealDef_Oreal, T, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.50 Z, X ) ) }.
% 0.89/1.50 { c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex,
% 0.89/1.50 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex(
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.89/1.50 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.89/1.50 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.89/1.50 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.89/1.50 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.89/1.50 tc_RealDef_Oreal, T, Y ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal
% 0.89/1.50 , Z, X ) ) }.
% 0.89/1.50 { c_RealVector_Odist__class_Odist( tc_Complex_Ocomplex, Y, X ) =
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) ) }.
% 0.89/1.50 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.89/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.50 X, Y, Z ) }.
% 0.89/1.50 { c_Complex_Ocomplex_Ocomplex__size( c_Complex_Ocomplex_OComplex( Y, X ) )
% 0.89/1.50 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.50 { c_Complex_Ocomplex_Ocomplex__rec( T, Z, c_Complex_Ocomplex_OComplex( Y, X
% 0.89/1.50 ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.89/1.50 { c_Complex_Ocomplex_Ocomplex__case( T, Z, c_Complex_Ocomplex_OComplex( Y,
% 0.89/1.50 X ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.89/1.50 { c_Nat_Osize__class_Osize( tc_Complex_Ocomplex,
% 0.89/1.50 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.50 tc_Nat_Onat ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol5( T, U, W ) ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol5( X, Y, Z
% 0.89/1.50 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, T ) }.
% 0.89/1.50 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.50 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol5( X, Y, Z
% 0.89/1.50 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, T, Z ) }.
% 0.89/1.50 { c_RealVector_OscaleR__class_OscaleR( tc_Complex_Ocomplex, Y, X ) =
% 0.89/1.50 c_Complex_Ocomplex_OComplex( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.50 tc_RealDef_Oreal ), Y ), c_Complex_ORe( X ) ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), c_Complex_OIm( X
% 0.89/1.50 ) ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.50 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.89/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.89/1.50 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.50 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.50 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.89/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.89/1.50 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.89/1.50 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.89/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.89/1.51 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.89/1.51 }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.89/1.51 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.89/1.51 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.89/1.51 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.51 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.89/1.51 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.51 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.89/1.51 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.89/1.51 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.51 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.51 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.51 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.89/1.51 ), U = Z, T = Y }.
% 0.89/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.51 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.89/1.51 ) }.
% 0.89/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.51 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.89/1.51 ) }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.89/1.51 ) ), Z ) }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.89/1.51 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.51 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.89/1.51 ) }.
% 0.89/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.51 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.89/1.51 ), ! U = T }.
% 0.89/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.51 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.89/1.51 ), ! Z = Y }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.51 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.89/1.51 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.89/1.51 ) ), T ), Y ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.89/1.51 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.89/1.51 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.89/1.51 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.89/1.51 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.89/1.51 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.89/1.51 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.89/1.51 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.89/1.51 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.89/1.51 ( X, Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.89/1.51 ) ), Y ) }.
% 0.89/1.51 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.89/1.51 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.89/1.51 ( X, Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.89/1.51 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.89/1.51 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.89/1.51 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.89/1.51 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.89/1.51 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.89/1.51 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.89/1.51 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.89/1.51 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.89/1.51 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.89/1.51 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.89/1.51 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.89/1.51 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.51 X, T, Z ) ), Y ) = c_RealVector_OscaleR__class_OscaleR( X, T, hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.51 X, T, Z ) ), Y ) = c_RealVector_OscaleR__class_OscaleR( X, T, hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.51 X, T, Z ) ), Y ) = c_RealVector_OscaleR__class_OscaleR( X, T, hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ),
% 0.89/1.51 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) =
% 0.89/1.51 c_RealVector_OscaleR__class_OscaleR( X, Z, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ),
% 0.89/1.51 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) =
% 0.89/1.51 c_RealVector_OscaleR__class_OscaleR( X, Z, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ),
% 0.89/1.51 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) =
% 0.89/1.51 c_RealVector_OscaleR__class_OscaleR( X, Z, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.51 c_RealVector_OscaleR__class_OscaleR( X, T,
% 0.89/1.51 c_RealVector_OscaleR__class_OscaleR( X, Z, Y ) ) =
% 0.89/1.51 c_RealVector_OscaleR__class_OscaleR( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Z ), Y ) }.
% 0.89/1.51 { c_RealVector_OscaleR__class_OscaleR( tc_RealDef_Oreal, Y, X ) = hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.51 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha1( X, Y
% 0.89/1.51 , Z ), alpha10( X, Y, Z ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.51 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ), alpha10( X, Y, Z ) }.
% 0.89/1.51 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.89/1.51 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), Y ), alpha1( X, Y, Z ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( X ) ), alpha2( X, Y, Z ), alpha11( X, Y, Z ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( X ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha11( X, Y, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( X ) ) }.
% 0.89/1.51 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.51 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( X ), Y ), alpha11( X, Y, Z ) }.
% 0.89/1.51 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.89/1.51 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ), alpha2( X, Y, Z ) }.
% 0.89/1.51 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( X ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.51 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__semiring( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.51 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__semiring( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.51 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.51 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__semiring( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__semiring( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.51 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.51 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( X ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha3( X, Y, Z, T ),
% 0.89/1.51 alpha12( X, Y, Z, T ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha12( X, Y, Z, T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.51 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha12( X, Y, Z, T ) }.
% 0.89/1.51 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.89/1.51 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.51 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha3( X, Y, Z, T ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha4( X, Y, Z, T ),
% 0.89/1.51 alpha13( X, Y, Z, T ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha13( X, Y, Z, T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.51 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha13( X, Y, Z, T ) }.
% 0.89/1.51 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.89/1.51 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.89/1.51 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha4( X, Y, Z, T ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.51 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.51 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.51 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.51 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.51 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.51 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( X ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.51 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.51 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( X ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.89/1.51 .
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.89/1.51 .
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.51 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.51 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.51 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.51 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( X ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.51 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.51 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.89/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.51 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.89/1.51 Z ) ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.89/1.51 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.89/1.51 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.89/1.51 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.89/1.51 W ) ), U ), Y ) }.
% 0.89/1.51 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.89/1.51 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), Z ), U ), Y ) }.
% 0.89/1.51 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.89/1.51 Z ) ), U ), T ) = Y }.
% 0.89/1.51 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.89/1.51 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), Z ), U ), Y ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.51 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.89/1.51 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.89/1.51 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.51 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.89/1.51 { c_Complex_ORe( c_RealVector_OscaleR__class_OscaleR( tc_Complex_Ocomplex,
% 0.89/1.51 Y, X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal )
% 0.89/1.51 , Y ), c_Complex_ORe( X ) ) }.
% 0.89/1.51 { c_Complex_OIm( c_RealVector_OscaleR__class_OscaleR( tc_Complex_Ocomplex,
% 0.89/1.51 Y, X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal )
% 0.89/1.51 , Y ), c_Complex_OIm( X ) ) }.
% 0.89/1.51 { c_RealVector_OscaleR__class_OscaleR( tc_Complex_Ocomplex, Z,
% 0.89/1.51 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex( hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ), hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.51 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.51 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.51 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.51 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.89/1.51 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.89/1.51 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.89/1.51 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.51 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.51 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.51 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.51 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.89/1.51 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.51 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.89/1.51 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.89/1.51 ( X, Z, W ) ), U ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.89/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.89/1.51 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.89/1.51 X, W, Z ) ), U ), T ), Y ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), Z ), U ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring__abs( X ), alpha18( X, Z ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.51 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.89/1.51 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oordered__ring__abs( X ), alpha18( X, Z ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.89/1.51 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.51 { ! alpha18( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.51 { ! alpha18( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.51 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( X ) ), alpha18( X, Y ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.89/1.51 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.51 X, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal
% 0.89/1.51 ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.89/1.51 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.89/1.51 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.51 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.89/1.51 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.89/1.51 c_Complex_Ocomplex_OComplex( T, Z ) ), c_Complex_Ocomplex_OComplex( Y, X
% 0.89/1.51 ) ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.89/1.51 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_RealDef_Oreal ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_RealDef_Oreal ), Z ), X ) ), c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_RealDef_Oreal ), T ), X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_RealDef_Oreal ), Z ), Y ) ) ) }.
% 0.89/1.51 { c_Complex_OIm( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_Complex_Ocomplex ), Y ), X ) ) = c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_RealDef_Oreal ), c_Complex_ORe( Y ) ), c_Complex_OIm( X ) ), hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Complex_OIm( Y
% 0.89/1.51 ) ), c_Complex_ORe( X ) ) ) }.
% 0.89/1.51 { c_Complex_ORe( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_Complex_Ocomplex ), Y ), X ) ) = c_Groups_Ominus__class_Ominus(
% 0.89/1.51 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_RealDef_Oreal ), c_Complex_ORe( Y ) ), c_Complex_ORe( X ) ), hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Complex_OIm( Y
% 0.89/1.51 ) ), c_Complex_OIm( X ) ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), X
% 0.89/1.51 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.89/1.51 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_RealDef_Oreal ), c_Complex_ORe( Y ) ), c_Complex_ORe( X ) ), hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Complex_OIm( Y
% 0.89/1.51 ) ), c_Complex_OIm( X ) ) ), c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_RealDef_Oreal ), c_Complex_ORe( Y ) ), c_Complex_OIm( X ) ), hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Complex_OIm( Y
% 0.89/1.51 ) ), c_Complex_ORe( X ) ) ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.89/1.51 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.89/1.51 ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.89/1.51 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.89/1.51 ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol6 ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, c_Complex_OIm( X ) ),
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol6 ) ) }
% 0.89/1.51 .
% 0.89/1.51 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7 ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, c_Complex_ORe( X ) ),
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol7 ) ) }
% 0.89/1.51 .
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol8( Z, T ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.51 X, Z, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal
% 0.89/1.51 ), c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Z ) ), skol8( X, Y
% 0.89/1.51 ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol9( Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.51 X, Y, Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal
% 0.89/1.51 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol9( X ) ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10 ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, c_Complex_OIm( X ) ),
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol10 ) ) }
% 0.89/1.51 .
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Z, X ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.89/1.51 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.89/1.51 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.51 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.51 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.89/1.51 ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.51 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.89/1.51 ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.51 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.89/1.51 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.51 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.89/1.51 ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.89/1.51 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.89/1.51 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.89/1.51 { alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.89/1.51 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.89/1.51 { alpha19( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.89/1.51 ( X, Y ), Z ) ) }.
% 0.89/1.51 { ! alpha19( X, Y, Z ), alpha22( X, Y, Z ), Z = Y }.
% 0.89/1.51 { ! alpha19( X, Y, Z ), alpha22( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.89/1.51 ) ) }.
% 0.89/1.51 { ! alpha22( X, Y, Z ), alpha19( X, Y, Z ) }.
% 0.89/1.51 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha19( X, Y, Z ) }.
% 0.89/1.51 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.89/1.51 }.
% 0.89/1.51 { ! alpha22( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.89/1.51 X, Y ), Z ) ), alpha22( X, Y, Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.89/1.51 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.89/1.51 , X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.89/1.51 .
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.89/1.51 .
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.89/1.51 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.89/1.51 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.89/1.51 .
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.89/1.51 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.89/1.51 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Z, Y ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Z, X ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.89/1.51 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.89/1.51 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.51 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.89/1.51 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.89/1.51 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol11( X, Y ) ) }.
% 0.89/1.51 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol12( X, Y ) ) }.
% 0.89/1.51 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.89/1.51 ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.89/1.51 ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.89/1.51 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.89/1.51 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 Y ), X ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.89/1.51 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.89/1.51 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.89/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.89/1.51 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.89/1.51 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.89/1.51 .
% 0.89/1.51 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.89/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.89/1.51 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.89/1.51 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.89/1.51 .
% 0.89/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.89/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), X ) = X }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ) ) = X }.
% 0.89/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.89/1.51 .
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.51 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.51 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.89/1.51 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.89/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.89/1.51 , alpha5( X, Y, Z ) }.
% 0.89/1.51 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.89/1.51 , alpha14( X, Y, Z ) }.
% 0.89/1.51 { ! alpha5( X, Y, Z ), ! alpha14( X, Y, Z ), hBOOL( hAPP( Z,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.89/1.51 { ! alpha14( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.89/1.51 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.89/1.51 { ! hBOOL( hAPP( Z, skol13( T, U, Z ) ) ), alpha14( X, Y, Z ) }.
% 0.89/1.51 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol13( X, Y, Z ) ),
% 0.89/1.51 alpha14( X, Y, Z ) }.
% 0.89/1.51 { ! alpha5( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.89/1.51 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha5( X, Y, Z ) }.
% 0.89/1.51 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha5
% 0.89/1.51 ( X, Y, Z ) }.
% 0.89/1.51 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.89/1.51 , ! alpha6( X, Y, Z ) }.
% 0.89/1.51 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.89/1.51 , ! alpha15( X, Y, Z ) }.
% 0.89/1.51 { alpha6( X, Y, Z ), alpha15( X, Y, Z ), hBOOL( hAPP( Z,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.89/1.51 { ! alpha15( X, Y, Z ), ! hBOOL( hAPP( Z, skol14( T, U, Z ) ) ) }.
% 0.89/1.51 { ! alpha15( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.89/1.51 skol14( X, Y, Z ) ) }.
% 0.89/1.51 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.89/1.51 ) ), alpha15( X, Y, Z ) }.
% 0.89/1.51 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.89/1.51 .
% 0.89/1.51 { ! alpha6( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ) ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6( X, Y, Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.89/1.51 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol15 ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, c_Complex_ORe( X ) ),
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol15 ) ) }
% 0.89/1.51 .
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol16( Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.51 X, Y, Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal
% 0.89/1.51 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol16( X ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol17( Z, T ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.51 X, Z, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal
% 0.89/1.51 ), c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Z ) ), skol17( X,
% 0.89/1.51 Y ) ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.89/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.89/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.89/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.51 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.89/1.51 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.51 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.89/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.89/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.89/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.89/1.51 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.89/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.89/1.51 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.89/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.89/1.51 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.89/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.89/1.51 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.89/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.89/1.51 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.89/1.51 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.89/1.51 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.89/1.51 .
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.89/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.89/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.89/1.51 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_Nat_Onat ), X ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.89/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.89/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.89/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.89/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.51 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.51 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.51 c_RealVector_Obounded__bilinear( X, Y, Z, T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol18( U, W, V0, V1 ) )
% 0.89/1.51 }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.51 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.51 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.51 c_RealVector_Obounded__bilinear( X, Y, Z, T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( Z, hAPP( hAPP( T, U ), W ) ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, U ) ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( Y, W ) ) ), skol18( X, Y, Z, T ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol19( Z, T ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.51 X, Y, Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal
% 0.89/1.51 ), c_RealVector_Onorm__class_Onorm( X, Z ) ), skol19( X, Y ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol20( Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol20( X ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol21( Z, T ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol21( X, Y ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol22( Z, T ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol22( X, Y ) ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, c_Complex_OIm( X ) ),
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol23 ) ) }
% 0.89/1.51 .
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, c_Complex_ORe( X ) ),
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol24 ) ) }
% 0.89/1.51 .
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.51 X, Z, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal
% 0.89/1.51 ), c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Z ) ), skol25( X,
% 0.89/1.51 Y ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.51 X, Y, Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal
% 0.89/1.51 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol26( X ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.51 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.51 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.51 c_RealVector_Obounded__bilinear( X, Y, Z, T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol27( U, W, V0, V1 ) )
% 0.89/1.51 }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.51 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.51 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.51 c_RealVector_Obounded__bilinear( X, Y, Z, T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( Z, hAPP( hAPP( T, U ), W ) ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, U ) ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( Y, W ) ) ), skol27( X, Y, Z, T ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol28( Z, T ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.51 X, Y, Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal
% 0.89/1.51 ), c_RealVector_Onorm__class_Onorm( X, Z ) ), skol28( X, Y ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol29( X ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol30( Z, T ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol30( X, Y ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol31( Z, T ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol31( X, Y ) ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.89/1.51 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.89/1.51 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 0.89/1.51 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.89/1.51 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( Z ), !
% 0.89/1.51 class_RealVector_Oreal__normed__vector( Y ), !
% 0.89/1.51 class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.51 c_RealVector_Obounded__bilinear( X, Y, Z, T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( Z, hAPP( hAPP( T, U ), W ) ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, U ) ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( Y, W ) ) ), skol32( X, Y, Z, T ) ) ) }.
% 0.89/1.51 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.89/1.51 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.89/1.51 }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.89/1.51 ), c_RComplete_Onatfloor( X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.89/1.51 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, c_RealVector_OscaleR__class_OscaleR(
% 0.89/1.51 X, Y, Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal
% 0.89/1.51 ), c_RealVector_Onorm__class_Onorm( X, Z ) ), skol33( X, Y ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol34( X ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol35( X, Y ) ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol36( X, Y ) ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.51 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.89/1.51 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.51 c_RComplete_Onatfloor( X ), Y ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.89/1.51 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.51 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.89/1.51 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.51 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 0.89/1.51 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 0.89/1.51 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.89/1.51 Y = X }.
% 0.89/1.51 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.89/1.51 , X ) }.
% 0.89/1.51 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.89/1.51 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.89/1.51 ( tc_Nat_Onat, X ) ) }.
% 0.89/1.51 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.89/1.51 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.89/1.51 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 0.89/1.51 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.89/1.51 , c_RComplete_Onatfloor( X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.89/1.51 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.89/1.51 , c_RComplete_Onatfloor( X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.89/1.51 c_RComplete_Onatfloor( X ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.51 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.89/1.51 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.89/1.51 c_RComplete_Onatceiling( X ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.89/1.51 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.89/1.51 c_RComplete_Onatfloor( X ) = Y }.
% 0.89/1.51 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.89/1.51 = Y }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.89/1.51 = Y }.
% 0.89/1.51 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.89/1.51 = Y }.
% 0.89/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.89/1.51 = Y }.
% 0.89/1.51 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.89/1.51 = Y }.
% 0.89/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.89/1.51 = Y }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.89/1.51 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.89/1.51 c_Groups_Oone__class_Oone( X ) }.
% 0.89/1.51 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.89/1.51 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.89/1.51 { ! class_RealVector_Oreal__vector( X ),
% 0.89/1.51 c_RealVector_OscaleR__class_OscaleR( X, c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_RealDef_Oreal ), Y ) = Y }.
% 0.89/1.51 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.89/1.51 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.89/1.51 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( X ) }.
% 0.89/1.51 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.51 c_Groups_Oone__class_Oone( X ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.89/1.51 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.89/1.51 .
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.89/1.51 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.89/1.51 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.89/1.51 ) }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.51 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.89/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.89/1.51 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.89/1.51 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.89/1.51 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.89/1.51 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.89/1.51 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.89/1.51 ) }.
% 0.89/1.51 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.89/1.51 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.89/1.51 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.89/1.51 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.89/1.51 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( X ) }.
% 0.89/1.51 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.89/1.51 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.89/1.51 ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.89/1.51 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.89/1.51 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.89/1.51 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.89/1.51 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.51 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.89/1.51 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.89/1.51 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.89/1.51 .
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.89/1.51 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.89/1.51 , X ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.89/1.51 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.89/1.51 ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.51 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.89/1.51 }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.89/1.51 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_RComplete_Onatceiling( Y ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.89/1.51 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.89/1.51 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.89/1.51 tc_Nat_Onat, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.51 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_RealDef_Oreal ) ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.51 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.89/1.51 , X ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.89/1.51 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.89/1.51 ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_RealDef_Oreal ) ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.89/1.51 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.89/1.51 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.89/1.51 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.51 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_RComplete_Onatceiling( X ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.89/1.51 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.51 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Nat_Onat ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.51 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.89/1.51 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.51 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.89/1.51 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.89/1.51 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.89/1.51 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.89/1.51 , Y ), X ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.89/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Nat_Onat ) }.
% 0.89/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Nat_Onat ) }.
% 0.89/1.51 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.89/1.51 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.89/1.51 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { c_Complex_OIm( c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.51 { c_Complex_ORe( c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.89/1.51 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.89/1.51 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.89/1.51 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.89/1.51 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.89/1.51 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.89/1.51 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.89/1.51 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Complex_Ocomplex ), Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.89/1.51 }.
% 0.89/1.51 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.89/1.51 ) }.
% 0.89/1.51 { ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), ! X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.51 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Complex_Ocomplex ) }.
% 0.89/1.51 { c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) =
% 0.89/1.51 c_Complex_Ocomplex_OComplex( c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 0.89/1.51 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.89/1.51 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.89/1.51 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.89/1.51 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.89/1.51 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol37( X ),
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, skol37( X ) ) ) }.
% 0.89/1.51 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.89/1.51 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol38( Z, Y
% 0.89/1.51 ), Y ) }.
% 0.89/1.51 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.89/1.51 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.89/1.51 skol38( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.89/1.51 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.89/1.51 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.89/1.51 , skol38( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.89/1.51 c_Complex_Oii ), c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 0.89/1.51 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 0.89/1.51 .
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.89/1.51 ), c_Orderings_Oord__class_Oless__eq( X, T, skol39( X, U, W, T ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.89/1.51 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.89/1.51 ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.89/1.51 hAPP( Z, T ), hAPP( Z, skol39( X, Y, Z, T ) ) ) ),
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.89/1.51 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.89/1.51 ) ) }.
% 0.89/1.51 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.89/1.51 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.89/1.51 { c_Complex_ORe( c_Complex_Oii ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_RealDef_Oreal ) }.
% 0.89/1.51 { c_Complex_OIm( c_Complex_Oii ) = c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_RealDef_Oreal ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.89/1.51 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 0.89/1.51 { c_Complex_Oii = c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_RealDef_Oreal ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.89/1.51 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, Y =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.51 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, X =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.89/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.89/1.51 c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.89/1.51 c_Complex_Ocomplex_OComplex( Y, X ) ), c_Complex_Oii ) =
% 0.89/1.51 c_Complex_Ocomplex_OComplex( c_Groups_Ouminus__class_Ouminus(
% 0.89/1.51 tc_RealDef_Oreal, X ), Y ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.89/1.51 c_Complex_Oii ), c_Complex_Ocomplex_OComplex( Y, X ) ) =
% 0.89/1.51 c_Complex_Ocomplex_OComplex( c_Groups_Ouminus__class_Ouminus(
% 0.89/1.51 tc_RealDef_Oreal, X ), Y ) }.
% 0.89/1.51 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.89/1.51 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.51 tc_Nat_Onat, skol40( X, Y ), skol60( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.89/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 hAPP( Y, skol60( X, Y ) ), hAPP( Y, skol40( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.89/1.51 , Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.89/1.51 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.89/1.51 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Z, Y ) ) }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Nat_Onat ) ) = Y }.
% 0.89/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.89/1.51 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.51 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.89/1.51 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.89/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.89/1.51 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.89/1.51 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( X ) }.
% 0.89/1.51 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.89/1.51 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.89/1.51 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.51 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.89/1.51 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.89/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.89/1.51 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.89/1.51 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.89/1.51 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.89/1.51 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.89/1.51 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.89/1.51 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.89/1.51 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.89/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.89/1.51 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.89/1.51 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.89/1.51 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.89/1.51 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.89/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.89/1.51 ), X ) ) }.
% 0.89/1.51 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.89/1.51 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.89/1.51 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.89/1.51 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.89/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.89/1.51 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.89/1.51 ( tc_Nat_Onat ) ) ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.89/1.51 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.89/1.51 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( X ) }.
% 0.89/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.89/1.51 = c_Groups_Oone__class_Oone( X ) }.
% 0.89/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.89/1.51 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.89/1.51 ) }.
% 0.89/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Nat_Onat ) ) = Y }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.51 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.51 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.89/1.51 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.89/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.89/1.51 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.89/1.51 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.89/1.51 .
% 0.89/1.51 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.89/1.51 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.89/1.51 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ) }.
% 0.89/1.51 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.89/1.51 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.89/1.51 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.89/1.51 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.89/1.51 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.89/1.51 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( X ) }.
% 0.89/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.89/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.89/1.51 ( hAPP( c_Power_Opower__class_Opower( X ),
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) =
% 0.89/1.51 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.89/1.51 ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.89/1.51 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.51 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.51 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.51 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.89/1.51 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.89/1.51 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.89/1.51 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.89/1.51 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.51 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.89/1.51 ) ) }.
% 0.89/1.51 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.89/1.51 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.51 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.51 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.89/1.51 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.89/1.51 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.89/1.51 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.51 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.89/1.51 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.51 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.89/1.51 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.89/1.51 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.89/1.51 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.89/1.51 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.89/1.51 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), Y ) }.
% 0.89/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.89/1.51 ), X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.89/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.89/1.51 tc_Int_Oint, Y ) ), X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.89/1.51 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.89/1.51 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.89/1.51 .
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.89/1.51 .
% 0.89/1.51 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Int_Oint ), X ) = X }.
% 0.89/1.51 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Int_Oint ) ) = X }.
% 0.89/1.51 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.89/1.51 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.89/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.89/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.89/1.51 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.89/1.51 tc_Int_Oint, X ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.89/1.51 tc_Int_Oint, X ) = X }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Int_Oint ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.89/1.51 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.89/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.89/1.51 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.89/1.51 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.89/1.51 ( tc_Int_Oint ) }.
% 0.89/1.51 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.89/1.51 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.89/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.89/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.89/1.51 = X }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Int_Oint ) ) ) }.
% 0.89/1.51 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Int_Oint ) ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.89/1.51 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Int_Oint ) ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.89/1.51 }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Int_Oint ) ), X ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.89/1.51 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.89/1.51 .
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.89/1.51 ( tc_Int_Oint ) ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.89/1.51 }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.89/1.51 tc_Int_Oint ) ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.51 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.89/1.51 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.89/1.51 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.89/1.51 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.89/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.89/1.51 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.89/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.89/1.51 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.89/1.51 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.89/1.51 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.89/1.51 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.89/1.51 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.89/1.51 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.89/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.89/1.51 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.89/1.51 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.89/1.51 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.89/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.89/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.51 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.89/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.89/1.51 ( tc_Int_Oint ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.89/1.51 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.89/1.51 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.89/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.89/1.51 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.89/1.51 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.89/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.89/1.51 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.89/1.52 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.89/1.52 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.89/1.52 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.89/1.52 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.89/1.52 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.89/1.52 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.89/1.52 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.89/1.52 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.89/1.52 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.89/1.52 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.89/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.89/1.52 tc_Int_Oint ) ) }.
% 0.89/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.89/1.52 tc_Int_Oint ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.89/1.52 tc_Int_Oint, X, Y ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.52 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.89/1.52 tc_Int_Oint, X, Y ) }.
% 0.89/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.52 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.89/1.52 ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.52 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol41( Z, Y ) ) ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.89/1.52 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.89/1.52 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.52 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.89/1.52 tc_Int_Oint, skol41( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.52 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.89/1.52 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.89/1.52 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.89/1.52 , Z ), X ) ) ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.89/1.52 ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.52 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.89/1.52 tc_Int_Oint, X, Y ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.52 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol42( Z, Y ) ) ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.89/1.52 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.89/1.52 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.52 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.89/1.52 tc_Int_Oint, skol42( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.52 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.89/1.52 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.89/1.52 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.89/1.52 ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol43( Z, T ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol43( X, Y ) ), X ) =
% 0.89/1.52 Y }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.89/1.52 skol43( X, Y ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol44( Z, T ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol44( X, Y ) ), X ) =
% 0.89/1.52 Y }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.52 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.89/1.52 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.89/1.52 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 0.89/1.52 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.89/1.52 ), X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.89/1.52 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! X = Y,
% 0.89/1.52 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.89/1.52 ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless(
% 0.89/1.52 tc_RealDef_Oreal, X, Y ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.89/1.52 ), c_Transcendental_Oln( Y ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.89/1.52 ( X ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.52 tc_RealDef_Oreal, X, Y ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.89/1.52 ( X ), c_Transcendental_Oln( Y ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.89/1.52 ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.89/1.52 ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.89/1.52 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.89/1.52 ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.89/1.52 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! X =
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 0.89/1.52 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.89/1.52 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.89/1.52 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.89/1.52 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.89/1.52 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.89/1.52 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.89/1.52 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.89/1.52 ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.89/1.52 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.52 tc_RealDef_Oreal ), X ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.89/1.52 tc_RealDef_Oreal, c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) )
% 0.89/1.52 }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.89/1.52 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) ), X ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol45( Z, T ) ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol45( X, Y ) ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol61( X, Y, Z ) ) ), Z ),
% 0.89/1.52 c_SEQ_OBseq( X, Y ) }.
% 0.89/1.52 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 0.89/1.52 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.52 tc_Nat_Onat, skol46( X, Y ), skol62( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.89/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.52 hAPP( Y, skol46( X, Y ) ), hAPP( Y, skol62( X, Y ) ) ), c_SEQ_Oincseq( X
% 0.89/1.52 , Y ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol47( Z, T ) ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.89/1.52 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y, skol63( X, Y ) ) )
% 0.89/1.52 ) ), skol47( X, Y ) ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.89/1.52 ( Y, skol66( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y
% 0.89/1.52 , T ) ) ) ), Z ), c_SEQ_OBseq( X, Y ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol48( Z, T ) ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.89/1.52 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, skol64( X, Y ) ) ) ),
% 0.89/1.52 skol48( X, Y ) ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.89/1.52 ( Y, skol67( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, T ) ) )
% 0.89/1.52 , Z ), c_SEQ_OBseq( X, Y ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol49( Z, T ) ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol49( X, Y ) ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol50( X, Y, Z ) ) ), Y ),
% 0.89/1.52 c_SEQ_OBseq( X, Z ) }.
% 0.89/1.52 { alpha20( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.89/1.52 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol51( T, Y, U ), Y ) }
% 0.89/1.52 .
% 0.89/1.52 { alpha20( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.89/1.52 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ), hAPP(
% 0.89/1.52 X, skol51( X, Y, Z ) ) = Z }.
% 0.89/1.52 { ! alpha20( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol52( Z
% 0.89/1.52 , Y ), Y ) }.
% 0.89/1.52 { ! alpha20( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.89/1.52 tc_Int_Oint, hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, skol52( X
% 0.89/1.52 , Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, skol52( X,
% 0.89/1.52 Y ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.89/1.52 ( tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X,
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oone__class_Oone(
% 0.89/1.52 tc_Nat_Onat ) ) ), hAPP( X, Z ) ) ), c_Groups_Oone__class_Oone(
% 0.89/1.52 tc_Int_Oint ) ), alpha20( X, Y ) }.
% 0.89/1.52 { alpha21( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.89/1.52 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol53( T, Y, U ), Y ) }
% 0.89/1.52 .
% 0.89/1.52 { alpha21( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.89/1.52 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ), hAPP(
% 0.89/1.52 X, skol53( X, Y, Z ) ) = Z }.
% 0.89/1.52 { ! alpha21( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol54( Z
% 0.89/1.52 , Y ), Y ) }.
% 0.89/1.52 { ! alpha21( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.52 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.89/1.52 tc_Int_Oint, hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, skol54( X
% 0.89/1.52 , Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, skol54( X,
% 0.89/1.52 Y ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.89/1.52 ( tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X,
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oone__class_Oone(
% 0.89/1.52 tc_Nat_Onat ) ) ), hAPP( X, Z ) ) ), c_Groups_Oone__class_Oone(
% 0.89/1.52 tc_Int_Oint ) ), alpha21( X, Y ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol55( U, W, V0, T )
% 0.89/1.52 ), c_SEQ_OBseq( X, Y ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol55( X, Y, Z, T ) ) ), Z
% 0.89/1.52 ), c_SEQ_OBseq( X, Y ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol56( X, Y, Z ) ) ), Z ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.89/1.52 tc_Nat_Onat, c_Nat_OSuc( skol65( X, Y ) ) ) ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol68( X, Y, Z ) ) ),
% 0.89/1.52 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol69( T, U ) ) }.
% 0.89/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol68( X, Y, Z ) ) ),
% 0.89/1.52 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol69( X, Y ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.89/1.52 X ) ) }.
% 0.89/1.52 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.52 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.89/1.52 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.89/1.52 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.52 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.52 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.52 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.89/1.52 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.52 X ), Y ), Z = Y }.
% 0.89/1.52 { ! class_Rings_Olinordered__semidom( X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.52 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.52 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.89/1.52 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.89/1.52 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.89/1.52 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.89/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.89/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.89/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.89/1.52 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.52 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.52 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.89/1.52 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.89/1.52 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.89/1.52 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.89/1.52 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.52 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.89/1.52 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.89/1.52 ) ) }.
% 0.89/1.52 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.89/1.52 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.89/1.52 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.89/1.52 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.89/1.52 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.89/1.52 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.89/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.89/1.52 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.89/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.89/1.52 ), X ) ) }.
% 0.89/1.52 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.89/1.52 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.52 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.89/1.52 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.89/1.52 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.89/1.52 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.89/1.52 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.89/1.52 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.89/1.52 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.89/1.52 .
% 0.89/1.52 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.89/1.52 .
% 0.89/1.52 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.89/1.52 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.89/1.52 X ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.89/1.52 }.
% 0.89/1.52 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.52 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.52 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.89/1.52 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.89/1.52 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.89/1.52 c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! alpha7( X, Y ), Y = c_Nat_OSuc( skol57( Z, Y ) ) }.
% 0.89/1.52 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol57( X,
% 0.89/1.52 Y ), X ) }.
% 0.89/1.52 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.89/1.52 ), alpha7( X, Y ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.52 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.52 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol58( X ) ) }.
% 0.89/1.52 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.89/1.52 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.89/1.52 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.89/1.52 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.89/1.52 { ! c_Nat_OSuc( X ) = X }.
% 0.89/1.52 { ! X = c_Nat_OSuc( X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.89/1.52 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.89/1.52 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.89/1.52 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.52 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.89/1.52 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.52 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.89/1.52 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.89/1.52 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.52 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.89/1.52 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.52 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.89/1.52 .
% 0.89/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.89/1.52 ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.89/1.52 , c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.89/1.52 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.89/1.52 }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.89/1.52 c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.89/1.52 ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.89/1.52 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.89/1.52 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.89/1.52 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.52 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.89/1.52 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.89/1.52 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.89/1.52 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.89/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.89/1.52 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.89/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.89/1.52 ), X ) ) }.
% 0.89/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.89/1.52 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.89/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.89/1.52 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.89/1.52 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.52 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.89/1.52 .
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.89/1.52 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol59( X, Y ) ) ) }.
% 0.89/1.52 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha8( X, Y ), alpha16
% 0.89/1.52 ( X, Y ) }.
% 0.89/1.52 { ! alpha8( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.89/1.52 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { ! alpha16( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.89/1.52 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.89/1.52 { ! alpha16( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.52 { ! alpha16( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.89/1.52 tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha16( X, Y ) }.
% 0.89/1.52 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.89/1.52 tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.52 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.89/1.52 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha9( X, Y ), alpha17( X
% 0.89/1.52 , Y ) }.
% 0.89/1.52 { ! alpha9( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.89/1.52 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! alpha17( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.89/1.52 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! alpha17( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.52 { ! alpha17( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.89/1.52 tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha17( X, Y ) }.
% 0.89/1.52 { ! alpha9( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.89/1.52 tc_Nat_Onat ) ) }.
% 0.89/1.52 { ! alpha9( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.52 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.89/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.52 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.89/1.52 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.89/1.52 ) ) = X }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.89/1.52 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.89/1.52 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.89/1.52 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.89/1.52 ( tc_fun( Y, X ) ) }.
% 0.89/1.52 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.89/1.52 ) ) }.
% 0.89/1.52 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.89/1.52 .
% 0.89/1.52 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.89/1.52 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.89/1.52 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.89/1.52 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.89/1.52 tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.89/1.52 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.89/1.52 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.89/1.52 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.89/1.52 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.89/1.52 { class_Power_Opower( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.89/1.52 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.89/1.52 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.89/1.52 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.89/1.52 tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.89/1.52 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.89/1.52 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.89/1.52 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.89/1.52 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.89/1.52 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.89/1.52 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.89/1.52 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.89/1.52 tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.89/1.52 .
% 0.89/1.52 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_RealVector_Oreal__algebra( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_RealVector_Ometric__space( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_RealVector_Oreal__vector( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_RealVector_Odist__norm( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Oabs__if( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.89/1.52 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.89/1.52 tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_RealVector_Oreal__algebra( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_RealVector_Ometric__space( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_RealVector_Oreal__vector( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_RealVector_Odist__norm( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.89/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w ),
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.89/1.52 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_w, v_z ) ),
% 0.89/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_z ) ) ) }.
% 0.89/1.52
% 0.89/1.52 *** allocated 15000 integers for clauses
% 0.89/1.52 *** allocated 22500 integers for clauses
% 0.89/1.52 *** allocated 33750 integers for clauses
% 0.89/1.52 *** allocated 50625 integers for clauses
% 0.89/1.52 *** allocated 75937 integers for clauses
% 0.89/1.52 percentage equality = 0.265846, percentage horn = 0.930987
% 0.89/1.52 This is a problem with some equality
% 0.89/1.52
% 0.89/1.52
% 0.89/1.52
% 0.89/1.52 Options Used:
% 0.89/1.52
% 0.89/1.52 useres = 1
% 0.89/1.52 useparamod = 1
% 0.89/1.52 useeqrefl = 1
% 0.89/1.52 useeqfact = 1
% 0.89/1.52 usefactor = 1
% 0.89/1.52 usesimpsplitting = 0
% 0.89/1.52 usesimpdemod = 5
% 0.89/1.52 usesimpres = 3
% 0.89/1.52
% 0.89/1.52 resimpinuse = 1000
% 0.89/1.52 resimpclauses = 20000
% 0.89/1.52 substype = eqrewr
% 0.89/1.52 backwardsubs = 1
% 0.89/1.52 selectoldest = 5
% 0.89/1.52
% 0.89/1.52 litorderings [0] = split
% 0.89/1.52 litorderings [1] = extend the termordering, first sorting on arguments
% 0.89/1.52
% 0.89/1.52 termordering = kbo
% 0.89/1.52
% 0.89/1.52 litapriori = 0
% 0.89/1.52 termapriori = 1
% 0.89/1.52 litaposteriori = 0
% 0.89/1.52 termaposteriori = 0
% 0.89/1.52 demodaposteriori = 0
% 0.89/1.52 ordereqreflfact = 0
% 0.89/1.52
% 0.89/1.52 litselect = negord
% 0.89/1.52
% 0.89/1.52 maxweight = 15
% 0.89/1.52 maxdepth = 30000
% 0.89/1.52 maxlength = 115
% 0.89/1.52 maxnrvars = 195
% 0.89/1.52 excuselevel = 1
% 0.89/1.52 increasemaxweight = 1
% 0.89/1.52
% 0.89/1.52 maxselected = 10000000
% 0.89/1.52 maxnrclauses = 10000000
% 0.89/1.52
% 0.89/1.52 showgenerated = 0
% 0.89/1.52 showkept = 0
% 0.89/1.52 showselected = 0
% 0.89/1.52 showdeleted = 0
% 0.89/1.52 showresimp = 1
% 0.89/1.52 showstatus = 2000
% 0.89/1.52
% 0.89/1.52 prologoutput = 0
% 0.89/1.52 nrgoals = 5000000
% 0.89/1.52 totalproof = 1
% 0.89/1.52
% 0.89/1.52 Symbols occurring in the translation:
% 0.89/1.52
% 0.89/1.52 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.89/1.52 . [1, 2] (w:1, o:212, a:1, s:1, b:0),
% 0.89/1.52 ! [4, 1] (w:0, o:121, a:1, s:1, b:0),
% 0.89/1.52 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.89/1.52 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.89/1.52 hAPP [38, 2] (w:1, o:236, a:1, s:1, b:0),
% 0.89/1.52 tc_RealDef_Oreal [39, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.89/1.52 tc_Complex_Ocomplex [40, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.89/1.52 v_w [41, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.89/1.52 v_z [42, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.89/1.52 c_Groups_Oplus__class_Oplus [43, 3] (w:1, o:293, a:1, s:1, b:0),
% 0.89/1.52 c_Groups_Ouminus__class_Ouminus [44, 2] (w:1, o:237, a:1, s:1, b:0),
% 0.89/1.52
% 0.89/1.52 c_RealVector_Onorm__class_Onorm [45, 2] (w:1, o:238, a:1, s:1, b:0),
% 0.89/1.52
% 0.89/1.52 c_Groups_Ominus__class_Ominus [46, 3] (w:1, o:294, a:1, s:1, b:0),
% 0.89/1.52 c_Orderings_Oord__class_Oless__eq [47, 3] (w:1, o:295, a:1, s:1, b:0)
% 0.89/1.52 ,
% 0.89/1.52 class_RealVector_Oreal__normed__vector [51, 1] (w:1, o:126, a:1, s:1
% 0.89/1.52 , b:0),
% 0.89/1.52 class_Orderings_Opreorder [52, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.89/1.52 class_Groups_Oordered__ab__semigroup__add__imp__le [57, 1] (w:1, o:
% 0.89/1.52 130, a:1, s:1, b:0),
% 0.89/1.52 class_Groups_Oordered__ab__semigroup__add [61, 1] (w:1, o:131, a:1
% 0.89/1.52 , s:1, b:0),
% 0.89/1.52 class_Groups_Ogroup__add [64, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.89/1.52 class_Groups_Oab__group__add [65, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.89/1.52 class_Groups_Oordered__ab__group__add [67, 1] (w:1, o:134, a:1, s:1
% 0.89/1.52 , b:0),
% 0.89/1.52 class_Orderings_Olinorder [68, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.89/1.52 class_Orderings_Oord [71, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.89/1.52 tc_fun [72, 2] (w:1, o:275, a:1, s:1, b:0),
% 0.89/1.52 class_Orderings_Oorder [73, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.89/1.52 class_Groups_Ocancel__semigroup__add [75, 1] (w:1, o:136, a:1, s:1
% 0.89/1.52 , b:0),
% 0.89/1.52 class_Groups_Ocancel__ab__semigroup__add [76, 1] (w:1, o:137, a:1, s:
% 0.89/1.52 1, b:0),
% 0.89/1.52 class_Groups_Oab__semigroup__add [77, 1] (w:1, o:138, a:1, s:1, b:0)
% 0.89/1.52 ,
% 0.89/1.52 class_Rings_Ocomm__ring__1 [81, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.89/1.52 class_Lattices_Oboolean__algebra [82, 1] (w:1, o:141, a:1, s:1, b:0)
% 0.89/1.52 ,
% 0.89/1.52 c_Groups_Oabs__class_Oabs [83, 2] (w:1, o:276, a:1, s:1, b:0),
% 0.89/1.52 class_Groups_Ouminus [85, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.89/1.52 class_Groups_Ominus [87, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.89/1.52 class_Rings_Ocomm__semiring__1 [88, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.89/1.52 class_Groups_Oordered__ab__group__add__abs [90, 1] (w:1, o:146, a:1
% 0.89/1.52 , s:1, b:0),
% 0.89/1.52 c_Complex_Orcis [95, 2] (w:1, o:277, a:1, s:1, b:0),
% 0.89/1.52 c_Groups_Ozero__class_Ozero [96, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.89/1.52 c_Orderings_Oord__class_Oless [97, 3] (w:1, o:296, a:1, s:1, b:0),
% 0.89/1.52 c_Complex_OIm [98, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.89/1.52 c_Complex_ORe [99, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.89/1.52 c_RealVector_OscaleR__class_OscaleR [100, 3] (w:1, o:297, a:1, s:1
% 0.89/1.52 , b:0),
% 0.89/1.52 c_RealVector_Obounded__bilinear [103, 4] (w:1, o:324, a:1, s:1, b:0)
% 0.89/1.52 ,
% 0.89/1.52 c_RealVector_Odist__class_Odist [104, 3] (w:1, o:298, a:1, s:1, b:0)
% 0.89/1.52 ,
% 0.89/1.52 class_Groups_Oordered__comm__monoid__add [105, 1] (w:1, o:150, a:1
% 0.89/1.52 , s:1, b:0),
% 0.89/1.52 class_Groups_Olinordered__ab__group__add [106, 1] (w:1, o:143, a:1
% 0.89/1.52 , s:1, b:0),
% 0.89/1.52 class_RealVector_Oreal__vector [107, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.89/1.52
% 0.89/1.52 class_RealVector_Ometric__space [109, 1] (w:1, o:152, a:1, s:1, b:0)
% 0.89/1.52 ,
% 0.89/1.52 class_Groups_Ozero [111, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.89/1.52 class_Groups_Oabs__if [112, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.89/1.52 class_Groups_Oordered__cancel__ab__semigroup__add [114, 1] (w:1, o:
% 0.89/1.52 155, a:1, s:1, b:0),
% 0.89/1.52 class_Groups_Ocomm__monoid__add [115, 1] (w:1, o:156, a:1, s:1, b:0)
% 0.89/1.52 ,
% 0.89/1.52 class_Groups_Omonoid__add [116, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.89/1.52 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.89/1.52 117, 1] (w:1, o:188, a:1, s:1, b:0),
% 0.89/1.52 class_RealVector_Odist__norm [121, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.89/1.52 class_Rings_Olinordered__idom [122, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.89/1.52 class_Rings_Olinordered__semidom [123, 1] (w:1, o:162, a:1, s:1, b:0)
% 0.89/1.52 ,
% 0.89/1.52 c_Complex_Ocomplex_OComplex [126, 2] (w:1, o:278, a:1, s:1, b:0),
% 0.89/1.52 c_Complex_Ocomplex_Ocomplex__size [133, 1] (w:1, o:189, a:1, s:1, b:0
% 0.89/1.52 ),
% 0.89/1.52 tc_Nat_Onat [134, 0] (w:1, o:87, a:1, s:1, b:0),
% 0.89/1.52 c_Complex_Ocomplex_Ocomplex__rec [136, 3] (w:1, o:299, a:1, s:1, b:0)
% 0.89/1.52 ,
% 0.89/1.52 c_Complex_Ocomplex_Ocomplex__case [137, 3] (w:1, o:300, a:1, s:1, b:0
% 0.89/1.52 ),
% 0.89/1.52 c_Nat_Osize__class_Osize [138, 2] (w:1, o:279, a:1, s:1, b:0),
% 0.89/1.52 c_Groups_Otimes__class_Otimes [139, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.89/1.52 class_RealVector_Oreal__normed__algebra [140, 1] (w:1, o:163, a:1, s:
% 0.89/1.52 1, b:0),
% 0.89/1.52 class_Lattices_Oab__semigroup__idem__mult [145, 1] (w:1, o:140, a:1
% 0.89/1.52 , s:1, b:0),
% 0.89/1.52 class_Groups_Oab__semigroup__mult [149, 1] (w:1, o:191, a:1, s:1, b:0
% 0.89/1.52 ),
% 0.89/1.52 class_RealVector_Oreal__normed__div__algebra [150, 1] (w:1, o:164, a:
% 0.89/1.52 1, s:1, b:0),
% 0.89/1.52 class_Rings_Ono__zero__divisors [151, 1] (w:1, o:171, a:1, s:1, b:0)
% 0.89/1.52 ,
% 0.89/1.52 class_Rings_Oring__no__zero__divisors [152, 1] (w:1, o:172, a:1, s:1
% 0.89/1.52 , b:0),
% 0.89/1.52 class_Rings_Omult__zero [153, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.89/1.52 class_Rings_Ocomm__semiring [157, 1] (w:1, o:173, a:1, s:1, b:0),
% 0.89/1.52 class_Rings_Osemiring [159, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.89/1.52 class_Rings_Oring [160, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.89/1.52 class_Rings_Oidom [161, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.89/1.52 class_RealVector_Oreal__algebra [162, 1] (w:1, o:179, a:1, s:1, b:0)
% 0.89/1.52 ,
% 0.89/1.52 class_Rings_Olinordered__ring [163, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.89/1.52 class_Rings_Olinordered__ring__strict [164, 1] (w:1, o:161, a:1, s:1
% 0.89/1.52 , b:0),
% 0.89/1.52 class_Rings_Oordered__cancel__semiring [165, 1] (w:1, o:180, a:1, s:1
% 0.89/1.52 , b:0),
% 0.89/1.52 class_Rings_Oordered__ring [166, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.89/1.52 class_Rings_Oordered__semiring [167, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.89/1.52
% 0.89/1.52 class_Rings_Oordered__comm__semiring [168, 1] (w:1, o:184, a:1, s:1
% 0.89/1.52 , b:0),
% 0.89/1.52 class_Rings_Olinordered__semiring__strict [169, 1] (w:1, o:165, a:1
% 0.89/1.52 , s:1, b:0),
% 0.89/1.52 class_Rings_Olinordered__comm__semiring__strict [170, 1] (w:1, o:166
% 0.89/1.52 , a:1, s:1, b:0),
% 0.89/1.52 class_Rings_Olinordered__semiring [173, 1] (w:1, o:167, a:1, s:1, b:0
% 0.89/1.52 ),
% 0.89/1.52 class_Rings_Oordered__ring__abs [174, 1] (w:1, o:182, a:1, s:1, b:0)
% 0.89/1.52 ,
% 0.89/1.52 hBOOL [188, 1] (w:1, o:192, a:1, s:1, b:0),
% 2.04/2.41 c_RComplete_Onatfloor [193, 1] (w:1, o:193, a:1, s:1, b:0),
% 2.04/2.41 c_Complex_Oexpi [194, 1] (w:1, o:194, a:1, s:1, b:0),
% 2.04/2.41 c_RealDef_Oreal [195, 2] (w:1, o:280, a:1, s:1, b:0),
% 2.04/2.41 c_RComplete_Onatceiling [196, 1] (w:1, o:195, a:1, s:1, b:0),
% 2.04/2.41 c_Groups_Oone__class_Oone [197, 1] (w:1, o:196, a:1, s:1, b:0),
% 2.04/2.41 class_Groups_Ocomm__monoid__mult [198, 1] (w:1, o:197, a:1, s:1, b:0)
% 2.04/2.41 ,
% 2.04/2.41 class_Groups_Omonoid__mult [199, 1] (w:1, o:198, a:1, s:1, b:0),
% 2.04/2.41 class_RealVector_Oreal__normed__algebra__1 [200, 1] (w:1, o:185, a:1
% 2.04/2.41 , s:1, b:0),
% 2.04/2.41 class_Groups_Oone [201, 1] (w:1, o:199, a:1, s:1, b:0),
% 2.04/2.41 class_Rings_Ozero__neq__one [202, 1] (w:1, o:186, a:1, s:1, b:0),
% 2.04/2.41 class_Rings_Oring__1__no__zero__divisors [203, 1] (w:1, o:175, a:1
% 2.04/2.41 , s:1, b:0),
% 2.04/2.41 class_Rings_Oring__1 [204, 1] (w:1, o:176, a:1, s:1, b:0),
% 2.04/2.41 class_Rings_Olinordered__semiring__1 [206, 1] (w:1, o:168, a:1, s:1
% 2.04/2.41 , b:0),
% 2.04/2.41 class_Rings_Olinordered__semiring__1__strict [207, 1] (w:1, o:169, a:
% 2.04/2.41 1, s:1, b:0),
% 2.04/2.41 c_Complex_Oii [209, 0] (w:1, o:108, a:1, s:1, b:0),
% 2.04/2.41 c_SEQ_Odecseq [212, 2] (w:1, o:281, a:1, s:1, b:0),
% 2.04/2.41 c_Power_Opower__class_Opower [214, 1] (w:1, o:200, a:1, s:1, b:0),
% 2.04/2.41 class_Power_Opower [217, 1] (w:1, o:201, a:1, s:1, b:0),
% 2.04/2.41 tc_Int_Oint [218, 0] (w:1, o:112, a:1, s:1, b:0),
% 2.04/2.41 class_Rings_Osemiring__0 [219, 1] (w:1, o:187, a:1, s:1, b:0),
% 2.04/2.41 c_Power_Opower_Opower [221, 3] (w:1, o:301, a:1, s:1, b:0),
% 2.04/2.41 c_Nat__Transfer_Otsub [228, 2] (w:1, o:282, a:1, s:1, b:0),
% 2.04/2.41 c_Transcendental_Oln [230, 1] (w:1, o:202, a:1, s:1, b:0),
% 2.04/2.41 c_SEQ_OBseq [231, 2] (w:1, o:283, a:1, s:1, b:0),
% 2.04/2.41 c_SEQ_Oincseq [232, 2] (w:1, o:284, a:1, s:1, b:0),
% 2.04/2.41 c_Nat_OSuc [236, 1] (w:1, o:203, a:1, s:1, b:0),
% 2.04/2.41 tc_HOL_Obool [244, 0] (w:1, o:111, a:1, s:1, b:0),
% 2.04/2.41 alpha1 [245, 3] (w:1, o:302, a:1, s:1, b:1),
% 2.04/2.41 alpha2 [246, 3] (w:1, o:308, a:1, s:1, b:1),
% 2.04/2.41 alpha3 [247, 4] (w:1, o:325, a:1, s:1, b:1),
% 2.04/2.41 alpha4 [248, 4] (w:1, o:326, a:1, s:1, b:1),
% 2.04/2.41 alpha5 [249, 3] (w:1, o:309, a:1, s:1, b:1),
% 2.04/2.41 alpha6 [250, 3] (w:1, o:310, a:1, s:1, b:1),
% 2.04/2.41 alpha7 [251, 2] (w:1, o:285, a:1, s:1, b:1),
% 2.04/2.41 alpha8 [252, 2] (w:1, o:286, a:1, s:1, b:1),
% 2.04/2.41 alpha9 [253, 2] (w:1, o:287, a:1, s:1, b:1),
% 2.04/2.41 alpha10 [254, 3] (w:1, o:303, a:1, s:1, b:1),
% 2.04/2.41 alpha11 [255, 3] (w:1, o:304, a:1, s:1, b:1),
% 2.04/2.41 alpha12 [256, 4] (w:1, o:327, a:1, s:1, b:1),
% 2.04/2.41 alpha13 [257, 4] (w:1, o:328, a:1, s:1, b:1),
% 2.04/2.41 alpha14 [258, 3] (w:1, o:305, a:1, s:1, b:1),
% 2.04/2.41 alpha15 [259, 3] (w:1, o:306, a:1, s:1, b:1),
% 2.04/2.41 alpha16 [260, 2] (w:1, o:288, a:1, s:1, b:1),
% 2.04/2.41 alpha17 [261, 2] (w:1, o:289, a:1, s:1, b:1),
% 2.04/2.41 alpha18 [262, 2] (w:1, o:290, a:1, s:1, b:1),
% 2.04/2.41 alpha19 [263, 3] (w:1, o:307, a:1, s:1, b:1),
% 2.04/2.41 alpha20 [264, 2] (w:1, o:291, a:1, s:1, b:1),
% 2.04/2.41 alpha21 [265, 2] (w:1, o:292, a:1, s:1, b:1),
% 2.04/2.41 alpha22 [266, 3] (w:1, o:311, a:1, s:1, b:1),
% 2.04/2.41 skol1 [267, 2] (w:1, o:239, a:1, s:1, b:1),
% 2.04/2.41 skol2 [268, 3] (w:1, o:314, a:1, s:1, b:1),
% 2.04/2.41 skol3 [269, 3] (w:1, o:315, a:1, s:1, b:1),
% 2.04/2.41 skol4 [270, 3] (w:1, o:316, a:1, s:1, b:1),
% 2.04/2.41 skol5 [271, 3] (w:1, o:317, a:1, s:1, b:1),
% 2.04/2.41 skol6 [272, 0] (w:1, o:12, a:1, s:1, b:1),
% 2.04/2.41 skol7 [273, 0] (w:1, o:13, a:1, s:1, b:1),
% 2.04/2.41 skol8 [274, 2] (w:1, o:240, a:1, s:1, b:1),
% 2.04/2.41 skol9 [275, 1] (w:1, o:204, a:1, s:1, b:1),
% 2.04/2.41 skol10 [276, 0] (w:1, o:14, a:1, s:1, b:1),
% 2.04/2.41 skol11 [277, 2] (w:1, o:241, a:1, s:1, b:1),
% 2.04/2.41 skol12 [278, 2] (w:1, o:242, a:1, s:1, b:1),
% 2.04/2.41 skol13 [279, 3] (w:1, o:312, a:1, s:1, b:1),
% 2.04/2.41 skol14 [280, 3] (w:1, o:313, a:1, s:1, b:1),
% 2.04/2.41 skol15 [281, 0] (w:1, o:15, a:1, s:1, b:1),
% 2.04/2.41 skol16 [282, 1] (w:1, o:205, a:1, s:1, b:1),
% 2.04/2.41 skol17 [283, 2] (w:1, o:243, a:1, s:1, b:1),
% 2.04/2.41 skol18 [284, 4] (w:1, o:329, a:1, s:1, b:1),
% 2.04/2.41 skol19 [285, 2] (w:1, o:244, a:1, s:1, b:1),
% 2.04/2.41 skol20 [286, 1] (w:1, o:206, a:1, s:1, b:1),
% 2.04/2.41 skol21 [287, 2] (w:1, o:245, a:1, s:1, b:1),
% 12.34/12.75 skol22 [288, 2] (w:1, o:246, a:1, s:1, b:1),
% 12.34/12.75 skol23 [289, 0] (w:1, o:16, a:1, s:1, b:1),
% 12.34/12.75 skol24 [290, 0] (w:1, o:17, a:1, s:1, b:1),
% 12.34/12.75 skol25 [291, 2] (w:1, o:247, a:1, s:1, b:1),
% 12.34/12.75 skol26 [292, 1] (w:1, o:207, a:1, s:1, b:1),
% 12.34/12.75 skol27 [293, 4] (w:1, o:330, a:1, s:1, b:1),
% 12.34/12.75 skol28 [294, 2] (w:1, o:248, a:1, s:1, b:1),
% 12.34/12.75 skol29 [295, 1] (w:1, o:208, a:1, s:1, b:1),
% 12.34/12.75 skol30 [296, 2] (w:1, o:249, a:1, s:1, b:1),
% 12.34/12.75 skol31 [297, 2] (w:1, o:250, a:1, s:1, b:1),
% 12.34/12.75 skol32 [298, 4] (w:1, o:331, a:1, s:1, b:1),
% 12.34/12.75 skol33 [299, 2] (w:1, o:251, a:1, s:1, b:1),
% 12.34/12.75 skol34 [300, 1] (w:1, o:209, a:1, s:1, b:1),
% 12.34/12.75 skol35 [301, 2] (w:1, o:252, a:1, s:1, b:1),
% 12.34/12.75 skol36 [302, 2] (w:1, o:253, a:1, s:1, b:1),
% 12.34/12.75 skol37 [303, 1] (w:1, o:210, a:1, s:1, b:1),
% 12.34/12.75 skol38 [304, 2] (w:1, o:254, a:1, s:1, b:1),
% 12.34/12.75 skol39 [305, 4] (w:1, o:332, a:1, s:1, b:1),
% 12.34/12.75 skol40 [306, 2] (w:1, o:255, a:1, s:1, b:1),
% 12.34/12.75 skol41 [307, 2] (w:1, o:256, a:1, s:1, b:1),
% 12.34/12.75 skol42 [308, 2] (w:1, o:257, a:1, s:1, b:1),
% 12.34/12.75 skol43 [309, 2] (w:1, o:258, a:1, s:1, b:1),
% 12.34/12.75 skol44 [310, 2] (w:1, o:259, a:1, s:1, b:1),
% 12.34/12.75 skol45 [311, 2] (w:1, o:260, a:1, s:1, b:1),
% 12.34/12.75 skol46 [312, 2] (w:1, o:261, a:1, s:1, b:1),
% 12.34/12.75 skol47 [313, 2] (w:1, o:262, a:1, s:1, b:1),
% 12.34/12.75 skol48 [314, 2] (w:1, o:263, a:1, s:1, b:1),
% 12.34/12.75 skol49 [315, 2] (w:1, o:264, a:1, s:1, b:1),
% 12.34/12.75 skol50 [316, 3] (w:1, o:318, a:1, s:1, b:1),
% 12.34/12.75 skol51 [317, 3] (w:1, o:319, a:1, s:1, b:1),
% 12.34/12.75 skol52 [318, 2] (w:1, o:265, a:1, s:1, b:1),
% 12.34/12.75 skol53 [319, 3] (w:1, o:320, a:1, s:1, b:1),
% 12.34/12.75 skol54 [320, 2] (w:1, o:266, a:1, s:1, b:1),
% 12.34/12.75 skol55 [321, 4] (w:1, o:333, a:1, s:1, b:1),
% 12.34/12.75 skol56 [322, 3] (w:1, o:321, a:1, s:1, b:1),
% 12.34/12.75 skol57 [323, 2] (w:1, o:267, a:1, s:1, b:1),
% 12.34/12.75 skol58 [324, 1] (w:1, o:211, a:1, s:1, b:1),
% 12.34/12.75 skol59 [325, 2] (w:1, o:268, a:1, s:1, b:1),
% 12.34/12.75 skol60 [326, 2] (w:1, o:269, a:1, s:1, b:1),
% 12.34/12.75 skol61 [327, 3] (w:1, o:322, a:1, s:1, b:1),
% 12.34/12.75 skol62 [328, 2] (w:1, o:270, a:1, s:1, b:1),
% 12.34/12.75 skol63 [329, 2] (w:1, o:271, a:1, s:1, b:1),
% 12.34/12.75 skol64 [330, 2] (w:1, o:272, a:1, s:1, b:1),
% 12.34/12.75 skol65 [331, 2] (w:1, o:273, a:1, s:1, b:1),
% 12.34/12.75 skol66 [332, 4] (w:1, o:334, a:1, s:1, b:1),
% 12.34/12.75 skol67 [333, 4] (w:1, o:335, a:1, s:1, b:1),
% 12.34/12.75 skol68 [334, 3] (w:1, o:323, a:1, s:1, b:1),
% 12.34/12.75 skol69 [335, 2] (w:1, o:274, a:1, s:1, b:1).
% 12.34/12.75
% 12.34/12.75
% 12.34/12.75 Starting Search:
% 12.34/12.75
% 12.34/12.75 *** allocated 113905 integers for clauses
% 12.34/12.75 *** allocated 170857 integers for clauses
% 12.34/12.75 Resimplifying inuse:
% 12.34/12.75 Done
% 12.34/12.75
% 12.34/12.75
% 12.34/12.75 Intermediate Status:
% 12.34/12.75 Generated: 3368
% 12.34/12.75 Kept: 2106
% 12.34/12.75 Inuse: 95
% 12.34/12.75 Deleted: 1
% 12.34/12.75 Deletedinuse: 0
% 12.34/12.75
% 12.34/12.75 *** allocated 256285 integers for clauses
% 12.34/12.75 Resimplifying inuse:
% 12.34/12.75 Done
% 12.34/12.75
% 12.34/12.75 *** allocated 170857 integers for termspace/termends
% 12.34/12.75 Resimplifying inuse:
% 12.34/12.75 Done
% 12.34/12.75
% 12.34/12.75 *** allocated 384427 integers for clauses
% 12.34/12.75
% 12.34/12.75 Intermediate Status:
% 12.34/12.75 Generated: 9620
% 12.34/12.75 Kept: 4431
% 12.34/12.75 Inuse: 263
% 12.34/12.75 Deleted: 3
% 12.34/12.75 Deletedinuse: 0
% 12.34/12.75
% 12.34/12.75 Resimplifying inuse:
% 12.34/12.75 Done
% 12.34/12.75
% 12.34/12.75 Resimplifying inuse:
% 12.34/12.75 Done
% 12.34/12.75
% 12.34/12.75 *** allocated 256285 integers for termspace/termends
% 12.34/12.75
% 12.34/12.75 Intermediate Status:
% 12.34/12.75 Generated: 16621
% 12.34/12.75 Kept: 6456
% 12.34/12.75 Inuse: 317
% 12.34/12.75 Deleted: 4
% 12.34/12.75 Deletedinuse: 0
% 12.34/12.75
% 12.34/12.75 *** allocated 576640 integers for clauses
% 12.34/12.75 Resimplifying inuse:
% 12.34/12.75 Done
% 12.34/12.75
% 12.34/12.75
% 12.34/12.75 Intermediate Status:
% 12.34/12.75 Generated: 25613
% 12.34/12.75 Kept: 8707
% 12.34/12.75 Inuse: 392
% 12.34/12.75 Deleted: 11
% 12.34/12.75 Deletedinuse: 0
% 12.34/12.75
% 12.34/12.75 Resimplifying inuse:
% 12.34/12.75 Done
% 12.34/12.75
% 12.34/12.75 Resimplifying inuse:
% 12.34/12.75 Done
% 12.34/12.75
% 12.34/12.75 *** allocated 384427 integers for termspace/termends
% 12.34/12.75 *** allocated 864960 integers for clauses
% 12.34/12.75
% 12.34/12.75 Intermediate Status:
% 12.34/12.75 Generated: 33954
% 12.34/12.75 Kept: 10711
% 12.34/12.75 Inuse: 511
% 12.34/12.75 Deleted: 12
% 12.34/12.75 Deletedinuse: 0
% 12.34/12.75
% 12.34/12.75 Resimplifying inuse:
% 12.34/12.75 Done
% 12.34/12.75
% 12.34/12.75 Resimplifying inuse:
% 12.34/12.75 Done
% 12.34/12.75
% 12.34/12.75
% 12.34/12.75 Intermediate Status:
% 12.34/12.75 Generated: 44407
% 12.34/12.75 Kept: 12722
% 12.34/12.75 Inuse: 600
% 12.34/12.75 Deleted: 13
% 12.34/12.75 Deletedinuse: 0
% 12.34/12.75
% 12.34/12.75 Resimplifying inuse:
% 12.34/12.75 Done
% 12.34/12.75
% 12.34/12.75 *** allocated 576640 integers for termspace/termends
% 12.34/12.75
% 12.34/12.75 Intermediate Status:
% 12.34/12.75 Generated: 59732
% 12.34/12.75 Kept: 15662
% 12.34/12.75 Inuse: 667
% 12.34/12.75 Deleted: 14
% 12.34/12.75 Deletedinuse: 0
% 12.34/12.75
% 12.34/12.75 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 *** allocated 1297440 integers for clauses
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 71888
% 41.42/41.83 Kept: 17687
% 41.42/41.83 Inuse: 684
% 41.42/41.83 Deleted: 18
% 41.42/41.83 Deletedinuse: 1
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 83628
% 41.42/41.83 Kept: 19757
% 41.42/41.83 Inuse: 722
% 41.42/41.83 Deleted: 20
% 41.42/41.83 Deletedinuse: 1
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 88420
% 41.42/41.83 Kept: 21821
% 41.42/41.83 Inuse: 732
% 41.42/41.83 Deleted: 20
% 41.42/41.83 Deletedinuse: 1
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying clauses:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 *** allocated 864960 integers for termspace/termends
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 100107
% 41.42/41.83 Kept: 25601
% 41.42/41.83 Inuse: 772
% 41.42/41.83 Deleted: 352
% 41.42/41.83 Deletedinuse: 1
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 *** allocated 1946160 integers for clauses
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 106916
% 41.42/41.83 Kept: 27615
% 41.42/41.83 Inuse: 813
% 41.42/41.83 Deleted: 352
% 41.42/41.83 Deletedinuse: 1
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 114738
% 41.42/41.83 Kept: 30019
% 41.42/41.83 Inuse: 852
% 41.42/41.83 Deleted: 352
% 41.42/41.83 Deletedinuse: 1
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 121917
% 41.42/41.83 Kept: 32570
% 41.42/41.83 Inuse: 872
% 41.42/41.83 Deleted: 352
% 41.42/41.83 Deletedinuse: 1
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 129203
% 41.42/41.83 Kept: 35046
% 41.42/41.83 Inuse: 902
% 41.42/41.83 Deleted: 352
% 41.42/41.83 Deletedinuse: 1
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 137442
% 41.42/41.83 Kept: 37055
% 41.42/41.83 Inuse: 960
% 41.42/41.83 Deleted: 352
% 41.42/41.83 Deletedinuse: 1
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 *** allocated 1297440 integers for termspace/termends
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 143956
% 41.42/41.83 Kept: 39180
% 41.42/41.83 Inuse: 982
% 41.42/41.83 Deleted: 352
% 41.42/41.83 Deletedinuse: 1
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 *** allocated 2919240 integers for clauses
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 156564
% 41.42/41.83 Kept: 43224
% 41.42/41.83 Inuse: 1027
% 41.42/41.83 Deleted: 352
% 41.42/41.83 Deletedinuse: 1
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying clauses:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 163096
% 41.42/41.83 Kept: 45369
% 41.42/41.83 Inuse: 1032
% 41.42/41.83 Deleted: 681
% 41.42/41.83 Deletedinuse: 1
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 174348
% 41.42/41.83 Kept: 47520
% 41.42/41.83 Inuse: 1087
% 41.42/41.83 Deleted: 681
% 41.42/41.83 Deletedinuse: 1
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 185776
% 41.42/41.83 Kept: 49545
% 41.42/41.83 Inuse: 1128
% 41.42/41.83 Deleted: 682
% 41.42/41.83 Deletedinuse: 2
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 191576
% 41.42/41.83 Kept: 51756
% 41.42/41.83 Inuse: 1139
% 41.42/41.83 Deleted: 682
% 41.42/41.83 Deletedinuse: 2
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 198126
% 41.42/41.83 Kept: 55217
% 41.42/41.83 Inuse: 1142
% 41.42/41.83 Deleted: 682
% 41.42/41.83 Deletedinuse: 2
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 204321
% 41.42/41.83 Kept: 57236
% 41.42/41.83 Inuse: 1165
% 41.42/41.83 Deleted: 682
% 41.42/41.83 Deletedinuse: 2
% 41.42/41.83
% 41.42/41.83 *** allocated 1946160 integers for termspace/termends
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 210442
% 41.42/41.83 Kept: 59862
% 41.42/41.83 Inuse: 1182
% 41.42/41.83 Deleted: 682
% 41.42/41.83 Deletedinuse: 2
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 222145
% 41.42/41.83 Kept: 64713
% 41.42/41.83 Inuse: 1217
% 41.42/41.83 Deleted: 682
% 41.42/41.83 Deletedinuse: 2
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 Resimplifying clauses:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83 *** allocated 4378860 integers for clauses
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 229295
% 41.42/41.83 Kept: 68488
% 41.42/41.83 Inuse: 1222
% 41.42/41.83 Deleted: 1288
% 41.42/41.83 Deletedinuse: 2
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 235407
% 41.42/41.83 Kept: 70927
% 41.42/41.83 Inuse: 1237
% 41.42/41.83 Deleted: 1288
% 41.42/41.83 Deletedinuse: 2
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 240776
% 41.42/41.83 Kept: 73573
% 41.42/41.83 Inuse: 1247
% 41.42/41.83 Deleted: 1288
% 41.42/41.83 Deletedinuse: 2
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 246141
% 41.42/41.83 Kept: 76083
% 41.42/41.83 Inuse: 1257
% 41.42/41.83 Deleted: 1288
% 41.42/41.83 Deletedinuse: 2
% 41.42/41.83
% 41.42/41.83 Resimplifying inuse:
% 41.42/41.83 Done
% 41.42/41.83
% 41.42/41.83
% 41.42/41.83 Intermediate Status:
% 41.42/41.83 Generated: 252000
% 41.42/41.83 Kept: 78609
% 41.42/41.83 Inuse: 1272
% 106.94/107.38 Deleted: 1288
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 260089
% 106.94/107.38 Kept: 82538
% 106.94/107.38 Inuse: 1282
% 106.94/107.38 Deleted: 1288
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 269564
% 106.94/107.38 Kept: 84567
% 106.94/107.38 Inuse: 1306
% 106.94/107.38 Deleted: 1288
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying clauses:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 280660
% 106.94/107.38 Kept: 86606
% 106.94/107.38 Inuse: 1323
% 106.94/107.38 Deleted: 1409
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 288477
% 106.94/107.38 Kept: 88617
% 106.94/107.38 Inuse: 1349
% 106.94/107.38 Deleted: 1409
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 *** allocated 2919240 integers for termspace/termends
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 294617
% 106.94/107.38 Kept: 90855
% 106.94/107.38 Inuse: 1372
% 106.94/107.38 Deleted: 1409
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 307189
% 106.94/107.38 Kept: 93461
% 106.94/107.38 Inuse: 1382
% 106.94/107.38 Deleted: 1409
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 315693
% 106.94/107.38 Kept: 95627
% 106.94/107.38 Inuse: 1412
% 106.94/107.38 Deleted: 1409
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 320858
% 106.94/107.38 Kept: 98053
% 106.94/107.38 Inuse: 1420
% 106.94/107.38 Deleted: 1409
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 326063
% 106.94/107.38 Kept: 100064
% 106.94/107.38 Inuse: 1449
% 106.94/107.38 Deleted: 1409
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 333199
% 106.94/107.38 Kept: 102285
% 106.94/107.38 Inuse: 1467
% 106.94/107.38 Deleted: 1409
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 *** allocated 6568290 integers for clauses
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 340878
% 106.94/107.38 Kept: 104435
% 106.94/107.38 Inuse: 1487
% 106.94/107.38 Deleted: 1409
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying clauses:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 348033
% 106.94/107.38 Kept: 106861
% 106.94/107.38 Inuse: 1502
% 106.94/107.38 Deleted: 2022
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 354584
% 106.94/107.38 Kept: 108909
% 106.94/107.38 Inuse: 1532
% 106.94/107.38 Deleted: 2022
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 361313
% 106.94/107.38 Kept: 111053
% 106.94/107.38 Inuse: 1557
% 106.94/107.38 Deleted: 2022
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 367241
% 106.94/107.38 Kept: 113177
% 106.94/107.38 Inuse: 1582
% 106.94/107.38 Deleted: 2022
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 372573
% 106.94/107.38 Kept: 115306
% 106.94/107.38 Inuse: 1607
% 106.94/107.38 Deleted: 2022
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 378674
% 106.94/107.38 Kept: 117357
% 106.94/107.38 Inuse: 1632
% 106.94/107.38 Deleted: 2022
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 384106
% 106.94/107.38 Kept: 120553
% 106.94/107.38 Inuse: 1637
% 106.94/107.38 Deleted: 2022
% 106.94/107.38 Deletedinuse: 2
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 389581
% 106.94/107.38 Kept: 123790
% 106.94/107.38 Inuse: 1642
% 106.94/107.38 Deleted: 2023
% 106.94/107.38 Deletedinuse: 3
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 404369
% 106.94/107.38 Kept: 127918
% 106.94/107.38 Inuse: 1657
% 106.94/107.38 Deleted: 2023
% 106.94/107.38 Deletedinuse: 3
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying clauses:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 417070
% 106.94/107.38 Kept: 131702
% 106.94/107.38 Inuse: 1662
% 106.94/107.38 Deleted: 2897
% 106.94/107.38 Deletedinuse: 3
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 423419
% 106.94/107.38 Kept: 133707
% 106.94/107.38 Inuse: 1689
% 106.94/107.38 Deleted: 2897
% 106.94/107.38 Deletedinuse: 3
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 *** allocated 4378860 integers for termspace/termends
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 436280
% 106.94/107.38 Kept: 138957
% 106.94/107.38 Inuse: 1710
% 106.94/107.38 Deleted: 2897
% 106.94/107.38 Deletedinuse: 3
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38 Resimplifying inuse:
% 106.94/107.38 Done
% 106.94/107.38
% 106.94/107.38
% 106.94/107.38 Intermediate Status:
% 106.94/107.38 Generated: 447674
% 106.94/107.38 Kept: 140966
% 106.94/107.38 Inuse: 1723
% 208.65/209.15 Deleted: 2897
% 208.65/209.15 Deletedinuse: 3
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 454641
% 208.65/209.15 Kept: 143010
% 208.65/209.15 Inuse: 1742
% 208.65/209.15 Deleted: 2900
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 463240
% 208.65/209.15 Kept: 145229
% 208.65/209.15 Inuse: 1761
% 208.65/209.15 Deleted: 2901
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 469527
% 208.65/209.15 Kept: 147237
% 208.65/209.15 Inuse: 1794
% 208.65/209.15 Deleted: 2901
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 487418
% 208.65/209.15 Kept: 149843
% 208.65/209.15 Inuse: 1796
% 208.65/209.15 Deleted: 2901
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying clauses:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 505891
% 208.65/209.15 Kept: 152471
% 208.65/209.15 Inuse: 1801
% 208.65/209.15 Deleted: 3535
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 512896
% 208.65/209.15 Kept: 154492
% 208.65/209.15 Inuse: 1827
% 208.65/209.15 Deleted: 3535
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 553306
% 208.65/209.15 Kept: 158638
% 208.65/209.15 Inuse: 1836
% 208.65/209.15 Deleted: 3535
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 *** allocated 9852435 integers for clauses
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 562250
% 208.65/209.15 Kept: 160638
% 208.65/209.15 Inuse: 1851
% 208.65/209.15 Deleted: 3535
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 569186
% 208.65/209.15 Kept: 162706
% 208.65/209.15 Inuse: 1871
% 208.65/209.15 Deleted: 3535
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 600306
% 208.65/209.15 Kept: 167325
% 208.65/209.15 Inuse: 1891
% 208.65/209.15 Deleted: 3535
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 608156
% 208.65/209.15 Kept: 169346
% 208.65/209.15 Inuse: 1916
% 208.65/209.15 Deleted: 3535
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying clauses:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 614634
% 208.65/209.15 Kept: 171349
% 208.65/209.15 Inuse: 1949
% 208.65/209.15 Deleted: 3601
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 619340
% 208.65/209.15 Kept: 173516
% 208.65/209.15 Inuse: 1986
% 208.65/209.15 Deleted: 3601
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 623942
% 208.65/209.15 Kept: 175587
% 208.65/209.15 Inuse: 2021
% 208.65/209.15 Deleted: 3601
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 630736
% 208.65/209.15 Kept: 177589
% 208.65/209.15 Inuse: 2045
% 208.65/209.15 Deleted: 3601
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 637455
% 208.65/209.15 Kept: 179599
% 208.65/209.15 Inuse: 2059
% 208.65/209.15 Deleted: 3601
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 *** allocated 6568290 integers for termspace/termends
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 644784
% 208.65/209.15 Kept: 181801
% 208.65/209.15 Inuse: 2071
% 208.65/209.15 Deleted: 3601
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 659123
% 208.65/209.15 Kept: 183801
% 208.65/209.15 Inuse: 2081
% 208.65/209.15 Deleted: 3601
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 665828
% 208.65/209.15 Kept: 186171
% 208.65/209.15 Inuse: 2101
% 208.65/209.15 Deleted: 3601
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 670237
% 208.65/209.15 Kept: 188326
% 208.65/209.15 Inuse: 2141
% 208.65/209.15 Deleted: 3601
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying clauses:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 674504
% 208.65/209.15 Kept: 190407
% 208.65/209.15 Inuse: 2181
% 208.65/209.15 Deleted: 3950
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 680387
% 208.65/209.15 Kept: 192424
% 208.65/209.15 Inuse: 2200
% 208.65/209.15 Deleted: 3950
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 687751
% 208.65/209.15 Kept: 194869
% 208.65/209.15 Inuse: 2216
% 208.65/209.15 Deleted: 3950
% 208.65/209.15 Deletedinuse: 6
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15 Resimplifying inuse:
% 208.65/209.15 Done
% 208.65/209.15
% 208.65/209.15
% 208.65/209.15 Intermediate Status:
% 208.65/209.15 Generated: 69440Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------