TSTP Solution File: SWW179+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW179+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 23:21:04 EDT 2022
% Result : Timeout 300.03s 300.50s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SWW179+1 : TPTP v8.1.0. Released v5.2.0.
% 0.00/0.09 % Command : bliksem %s
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % DateTime : Sat Jun 4 17:11:32 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.97/1.35 *** allocated 10000 integers for termspace/termends
% 0.97/1.35 *** allocated 10000 integers for clauses
% 0.97/1.35 *** allocated 10000 integers for justifications
% 0.97/1.35 *** allocated 15000 integers for termspace/termends
% 0.97/1.35 *** allocated 22500 integers for termspace/termends
% 0.97/1.35 *** allocated 33750 integers for termspace/termends
% 0.97/1.35 Bliksem 1.12
% 0.97/1.35
% 0.97/1.35
% 0.97/1.35 Automatic Strategy Selection
% 0.97/1.35
% 0.97/1.35 *** allocated 50625 integers for termspace/termends
% 0.97/1.35 *** allocated 75937 integers for termspace/termends
% 0.97/1.35 *** allocated 113905 integers for termspace/termends
% 0.97/1.35
% 0.97/1.35 Clauses:
% 0.97/1.35
% 0.97/1.35 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_c____ ) ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), v_r ), v_m____ ) ) ) }
% 0.97/1.35 .
% 0.97/1.35 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.97/1.35 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.97/1.35 ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.97/1.35 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.35 , X ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.97/1.35 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.97/1.35 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.35 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.35 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.35 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.35 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.35 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.35 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.35 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.97/1.35 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_RealDef_Oreal ) ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.35 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.35 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.35 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.97/1.35 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( X ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.35 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.35 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.35 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( X ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( X ) ), alpha1( X, Y, Z ), alpha13( X, Y, Z ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( X ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha13( X, Y, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( X ) ) }.
% 0.97/1.35 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( X ), Y ), alpha13( X, Y, Z ) }.
% 0.97/1.35 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.35 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ), alpha1( X, Y, Z ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 0.97/1.35 , Z ), alpha14( X, Y, Z ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha14( X, Y, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ) }.
% 0.97/1.35 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.35 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.35 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semidom( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.35 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.35 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.35 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.35 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.35 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.35 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.35 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.35 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.35 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.35 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.35 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.35 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.35 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.97/1.35 { ! class_Rings_Oordered__ring__abs( X ), alpha35( X, Z ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.35 { ! class_Rings_Oordered__ring__abs( X ), alpha35( X, Z ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.35 { ! alpha35( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.35 { ! alpha35( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( X ) ), alpha35( X, Y ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.35 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.35 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.35 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.35 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.35 ( X, Y ) ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.97/1.35 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.35 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.97/1.35 ), Y ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.35 X, Y, Z ) }.
% 0.97/1.35 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.97/1.35 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.35 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.97/1.35 }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.97/1.35 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.97/1.35 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.97/1.35 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.35 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.35 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.35 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.35 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.35 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.35 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.35 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.35 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.97/1.35 ) ), T ), Y ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.35 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.35 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.35 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.35 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.97/1.35 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.35 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.97/1.35 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.97/1.35 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.97/1.35 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.97/1.35 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.97/1.35 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.97/1.35 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.97/1.35 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.35 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.35 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.97/1.35 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.97/1.35 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.35 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.35 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( X ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.35 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.97/1.35 .
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.35 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.35 .
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.35 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( X ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.35 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( X ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.35 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha3( X, Y, Z, T ),
% 0.97/1.35 alpha15( X, Y, Z, T ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z, T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.35 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.35 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha15( X, Y, Z, T ) }.
% 0.97/1.35 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.97/1.35 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.97/1.35 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha3( X, Y, Z, T ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha4( X, Y, Z, T ),
% 0.97/1.35 alpha16( X, Y, Z, T ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z, T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.35 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.35 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha16( X, Y, Z, T ) }.
% 0.97/1.35 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.35 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.35 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha4( X, Y, Z, T ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.35 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.35 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.35 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.35 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.35 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.35 .
% 0.97/1.35 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.35 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.97/1.35 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), v_r ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.97/1.35 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), X ) ), v_m____ ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.35 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.35 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.35 ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.35 ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.35 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol2 ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), v_r ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.97/1.35 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), X ) ), skol2 ) }.
% 0.97/1.35 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.97/1.35 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.35 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 T, Y ), Z = Y }.
% 0.97/1.35 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 T, Y ) }.
% 0.97/1.35 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 Y, Z ), T = Y }.
% 0.97/1.35 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 Y, Z ) }.
% 0.97/1.35 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 T, Y ), Z = Y }.
% 0.97/1.35 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 T, Y ), Z = Y }.
% 0.97/1.35 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 Y, T ), Z = Y }.
% 0.97/1.35 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.97/1.35 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.35 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.97/1.35 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.97/1.35 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.35 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.35 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.97/1.35 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.35 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.35 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.35 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.35 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.35 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.35 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.35 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.35 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.35 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.35 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, T, Y ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.35 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.35 , Y, Z ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, Z, Y ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.35 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.35 , T, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.35 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.35 , Y, T ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.35 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.35 , T, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.35 , T ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, Z, Y ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.35 ( X, Z, Y ) }.
% 0.97/1.35 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.35 = Y }.
% 0.97/1.35 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.35 = Y }.
% 0.97/1.35 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.35 = Y }.
% 0.97/1.35 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.35 = Y }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.97/1.35 ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.35 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.97/1.35 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.35 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.35 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.35 .
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.35 .
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.35 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 Y, Z ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 Z, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.35 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.35 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.35 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.35 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.35 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.97/1.35 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.35 , Y, T ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.35 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.35 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.35 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.35 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.35 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.97/1.35 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.35 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.35 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.35 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), v_r ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.97/1.35 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), X ) ), skol3 ) }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.97/1.35 , Y ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.35 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.35 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.97/1.35 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.35 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.35 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.97/1.35 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.35 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.97/1.35 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.97/1.35 ) ) }.
% 0.97/1.35 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.35 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.35 hAPP( Y, U ) ) }.
% 0.97/1.35 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.97/1.35 ( Z, skol4( X, Y, Z ) ), hAPP( Y, skol4( X, Y, Z ) ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.35 ( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.35 ( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.35 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.35 hAPP( Y, U ) ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.35 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.35 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.97/1.35 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.35 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.35 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.35 hAPP( Y, U ) ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.35 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.35 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.35 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.35 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.35 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.35 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.35 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.97/1.35 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.35 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.35 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.35 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.35 , ! Y = Z }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.35 , ! Z = Y }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.35 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.35 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.35 , ! Z = Y }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.35 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.35 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.35 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.35 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.35 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.35 Y ), ! Z = Y }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.35 Z ), ! Z = Y }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.35 Y ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.35 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.35 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.35 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.35 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.35 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.35 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.35 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.35 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.97/1.35 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.97/1.35 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.97/1.35 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.97/1.35 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.97/1.35 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.97/1.35 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.35 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.35 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.35 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.35 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.35 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.35 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.35 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.35 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.35 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.35 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.35 ( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.35 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.35 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.35 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.35 , ! Z = Y }.
% 0.97/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.35 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.35 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.35 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.35 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.35 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.35 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.35 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.35 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.35 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.35 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.35 ), U = Z, T = Y }.
% 0.97/1.35 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.35 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.35 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.35 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.35 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.97/1.35 ) ), Z ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.35 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.35 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.35 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.35 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.35 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.35 ), ! U = T }.
% 0.97/1.35 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.35 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.35 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.35 ), ! Z = Y }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.35 = Y }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.35 = Y }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.35 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.97/1.35 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.97/1.35 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol5( Z, T ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol5( X, Y ) ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol6( Z, T ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol6( X, Y ) ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7( Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol7( X ) ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol8( Z, T ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol8( X, Y ) ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol9( Z, T ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol9( X, Y ) ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10( Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol10( X ) ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol11( X, Y ) ) ) }.
% 0.97/1.35 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.35 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.97/1.35 .
% 0.97/1.35 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.35 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.97/1.35 }.
% 0.97/1.35 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.35 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.97/1.35 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.35 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.35 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.35 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol12( X ) ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol13( X, Y ) ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.35 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_RealDef_Oreal ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.35 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.97/1.35 tc_RealDef_Oreal ) }.
% 0.97/1.35 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.97/1.35 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 skol14( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, skol14( X, T, U ),
% 0.97/1.35 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.35 , Y ) }.
% 0.97/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), skol14( X, Y, Z ) ), Z ), Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.97/1.35 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.97/1.35 .
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.35 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.35 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.35 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.97/1.35 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.35 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.35 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.35 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.97/1.35 }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.97/1.35 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.97/1.35 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.35 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.97/1.35 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.35 .
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.35 .
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.35 .
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.97/1.35 .
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.97/1.35 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.97/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.97/1.35 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.35 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.35 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.35 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.35 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.35 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.35 { ! class_Fields_Olinordered__field( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , c_Groups_Ozero__class_Ozero( X ), skol15( X, T, U ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Fields_Olinordered__field( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 Y, skol15( X, Y, Z ) ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }
% 0.97/1.35 .
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.97/1.35 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.97/1.35 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.35 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.35 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.97/1.35 ( X, T, Y ) ) ) ) }.
% 0.97/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.35 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.35 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.35 }.
% 0.97/1.35 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.35 , ! alpha5( X, Y, Z ) }.
% 0.97/1.35 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.35 , ! alpha17( X, Y, Z ) }.
% 0.97/1.35 { alpha5( X, Y, Z ), alpha17( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.35 { ! alpha17( X, Y, Z ), ! hBOOL( hAPP( Z, skol16( T, U, Z ) ) ) }.
% 0.97/1.35 { ! alpha17( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.35 skol16( X, Y, Z ) ) }.
% 0.97/1.35 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.97/1.35 ) ), alpha17( X, Y, Z ) }.
% 0.97/1.35 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.97/1.35 .
% 0.97/1.35 { ! alpha5( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_Nat_Onat ) ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha5( X, Y, Z ) }.
% 0.97/1.35 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.35 , alpha6( X, Y, Z ) }.
% 0.97/1.35 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.35 , alpha18( X, Y, Z ) }.
% 0.97/1.35 { ! alpha6( X, Y, Z ), ! alpha18( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.35 { ! alpha18( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.35 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.35 { ! hBOOL( hAPP( Z, skol17( T, U, Z ) ) ), alpha18( X, Y, Z ) }.
% 0.97/1.35 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol17( X, Y, Z ) ),
% 0.97/1.35 alpha18( X, Y, Z ) }.
% 0.97/1.35 { ! alpha6( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.35 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha6( X, Y, Z ) }.
% 0.97/1.35 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6
% 0.97/1.35 ( X, Y, Z ) }.
% 0.97/1.35 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.35 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.35 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.35 tc_Polynomial_Opoly( X ), Y ) }.
% 0.97/1.35 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.35 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.35 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.97/1.35 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.35 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.35 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.35 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.35 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.35 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.35 ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.35 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.97/1.35 ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.35 X, Y ) }.
% 0.97/1.35 { alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.35 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.35 { alpha36( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.97/1.35 ( X, Y ), Z ) ) }.
% 0.97/1.35 { ! alpha36( X, Y, Z ), alpha40( X, Y, Z ), Z = Y }.
% 0.97/1.35 { ! alpha36( X, Y, Z ), alpha40( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.97/1.35 ) ) }.
% 0.97/1.35 { ! alpha40( X, Y, Z ), alpha36( X, Y, Z ) }.
% 0.97/1.35 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha36( X, Y, Z ) }.
% 0.97/1.35 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.97/1.35 }.
% 0.97/1.35 { ! alpha40( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.97/1.35 X, Y ), Z ) ), alpha40( X, Y, Z ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.35 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.35 ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.35 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.35 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.35 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.35 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.97/1.35 , X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.35 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.35 .
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.35 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.35 .
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.35 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.97/1.35 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.35 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.97/1.35 .
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.35 tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.35 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.97/1.35 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.35 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.35 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.97/1.35 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.35 , Y ) ) }.
% 0.97/1.35 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.35 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.35 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.97/1.35 X, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.35 X, Z, Y ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.35 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.97/1.35 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.35 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.97/1.35 ) }.
% 0.97/1.35 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.97/1.35 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.97/1.35 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.97/1.35 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.97/1.35 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol18( X
% 0.97/1.35 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol18( X, Y, Z ) ), Z =
% 0.97/1.35 Y }.
% 0.97/1.35 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.97/1.35 ) ) }.
% 0.97/1.35 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.97/1.35 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.97/1.35 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.97/1.35 c_Polynomial_Ocoeff( X, Y ) }.
% 0.97/1.35 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.35 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.97/1.35 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.97/1.35 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.97/1.35 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.35 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.35 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.35 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.35 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.35 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.35 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.35 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.35 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.97/1.35 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.35 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.35 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.35 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.97/1.35 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.35 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.35 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.35 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.35 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.35 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.35 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.35 tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.35 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.35 tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol19( X, Y ) ) }.
% 0.97/1.35 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol20( X, Y ) ) }.
% 0.97/1.35 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.35 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.97/1.35 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.35 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.35 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.35 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.35 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.35 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.35 = Y }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.35 ( X ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.35 , Y ) }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.35 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.35 ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.35 = Y }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.35 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.35 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.35 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.35 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.35 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.35 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.35 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.97/1.35 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.35 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.35 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.35 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.35 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.35 ( X, Y ), Z ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.35 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.35 ( X, Z ), Y ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.35 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.35 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.35 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.35 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.35 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.35 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.35 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.35 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.97/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.35 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.97/1.35 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.35 ( X, Y ) ) }.
% 0.97/1.35 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.97/1.35 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.35 ) ), Y ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.35 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.35 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.35 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.35 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.36 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.36 ( X, Y ) ) }.
% 0.97/1.36 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.36 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.36 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.36 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.36 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.36 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.36 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.36 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.97/1.36 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.36 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.97/1.36 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.36 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.36 Y ) ) = Y }.
% 0.97/1.36 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.36 Z, Y ) ) = Y }.
% 0.97/1.36 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.36 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.36 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.97/1.36 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.97/1.36 ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.36 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.97/1.36 ( X, Y, Z ) ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.36 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.97/1.36 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.36 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.97/1.36 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.36 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.97/1.36 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.36 tc_Polynomial_Opoly( X ), Y ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless(
% 0.97/1.36 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.97/1.36 tc_Polynomial_Opoly( X ), Y ) = Y }.
% 0.97/1.36 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.36 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.97/1.36 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.97/1.36 .
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.36 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.36 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.36 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.36 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( X ) ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.36 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.36 , Z, Y ) }.
% 0.97/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.36 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.36 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.36 ( X, Y ), Y ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.36 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.36 ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.36 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.36 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.36 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.36 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.36 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.36 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.36 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 , Y ) }.
% 0.97/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.36 , Y ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.36 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.36 .
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.36 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.36 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.36 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.36 X ) }.
% 0.97/1.36 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.36 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.36 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.36 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.97/1.36 ( X, Y ) }.
% 0.97/1.36 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.36 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.36 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.36 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.36 Z ) = Y }.
% 0.97/1.36 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.36 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.97/1.36 ( X, Z ) }.
% 0.97/1.36 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.36 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.36 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.36 Z ) ), Y ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.36 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.36 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.97/1.36 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.36 W ) ), U ), Y ) }.
% 0.97/1.36 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.36 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), Z ), U ), Y ) }.
% 0.97/1.36 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.36 Z ) ), U ), T ) = Y }.
% 0.97/1.36 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.36 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), Z ), U ), Y ) }.
% 0.97/1.36 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.97/1.36 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.36 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.36 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.36 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.36 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.36 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.97/1.36 ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.36 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.97/1.36 ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.36 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.97/1.36 ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.36 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.36 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.36 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.36 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.36 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.36 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.36 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.36 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.36 X, Z, Y ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.36 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.36 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.36 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 0.97/1.36 }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.97/1.36 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.97/1.36 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.97/1.36 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.36 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.97/1.36 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.36 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ) }.
% 0.97/1.36 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.97/1.36 ( tc_RealDef_Oreal, Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.97/1.36 , X ) ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ) }.
% 0.97/1.36 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.97/1.36 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.97/1.36 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.36 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.97/1.36 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.36 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.97/1.36 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.36 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.97/1.36 ( X ) ) ) }.
% 0.97/1.36 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.36 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.36 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.36 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.36 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.97/1.36 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.36 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.36 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.97/1.36 ( X, Z, W ) ), U ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.97/1.36 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.36 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.36 X, W, Z ) ), U ), T ), Y ) }.
% 0.97/1.36 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( X ), Z ), U ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.97/1.36 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.97/1.36 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.97/1.36 .
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.36 , c_Groups_Oabs__class_Oabs( X, Y ) ), c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.36 }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 ), c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.36 X, Y ) }.
% 0.97/1.36 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.36 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 0.97/1.36 }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.36 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.36 ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.97/1.36 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.97/1.36 ) }.
% 0.97/1.36 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.97/1.36 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.97/1.36 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.97/1.36 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.36 Y ) ) ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.36 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.36 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.36 ( X, Y ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.36 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.36 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.36 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.36 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.36 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.36 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.97/1.36 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z )
% 0.97/1.36 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) ) ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.97/1.36 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ),
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.97/1.36 ( tc_RealDef_Oreal, Z, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.97/1.36 , X ) ) ) ) ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.97/1.36 ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.36 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.97/1.36 ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.36 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.36 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.97/1.36 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.97/1.36 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.97/1.36 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.36 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.97/1.36 .
% 0.97/1.36 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.36 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.97/1.36 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.36 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.36 .
% 0.97/1.36 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.36 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), Z ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.36 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.36 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.36 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.36 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 Y ), X ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.97/1.36 .
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.97/1.36 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ) ) = X }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), X ) = X }.
% 0.97/1.36 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.36 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.36 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.36 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.36 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.36 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.36 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.36 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.36 .
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.36 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.36 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.36 }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.36 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.97/1.36 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.97/1.36 ( X, Z, Y ), T ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.36 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.97/1.36 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.97/1.36 ( X, Z, Y ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.36 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.36 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.97/1.36 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.97/1.36 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.36 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.36 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.36 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.36 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.36 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.36 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.97/1.36 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.36 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.36 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.36 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.97/1.36 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.97/1.36 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.36 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.36 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.36 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.97/1.36 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.97/1.36 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.36 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.36 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.36 , Y ), X ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.36 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Nat_Onat ) }.
% 0.97/1.36 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Nat_Onat ) }.
% 0.97/1.36 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.97/1.36 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.97/1.36 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.36 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.36 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.36 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.36 .
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.36 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.36 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.97/1.36 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.36 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.36 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.36 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.36 tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.36 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.97/1.36 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.97/1.36 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.36 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.97/1.36 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.97/1.36 }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.97/1.36 ), c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.36 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.36 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.97/1.36 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.97/1.36 ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.36 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.97/1.36 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.36 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.97/1.36 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.36 }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.97/1.36 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.97/1.36 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.36 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.97/1.36 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.36 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.36 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.97/1.36 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.36 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.97/1.36 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, X ) ) }.
% 0.97/1.36 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.97/1.36 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.97/1.36 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.97/1.36 Y = X }.
% 0.97/1.36 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.97/1.36 , X ) }.
% 0.97/1.36 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 0.97/1.36 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 0.97/1.36 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.36 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.36 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.36 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.36 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.36 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.97/1.36 ( tc_Nat_Onat, X ) ) }.
% 0.97/1.36 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.97/1.36 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.97/1.36 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.36 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.97/1.36 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 0.97/1.36 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.36 , c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.97/1.36 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 c_RComplete_Onatceiling( Y ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.36 tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_RealDef_Oreal ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.36 , X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.97/1.36 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.36 , c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.36 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 c_RComplete_Onatceiling( X ), Y ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_RealDef_Oreal ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.36 c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.36 c_RComplete_Onatceiling( X ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.97/1.36 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.97/1.36 c_RComplete_Onatfloor( X ) = Y }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.97/1.36 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol21( X ),
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, skol21( X ) ) ) }.
% 0.97/1.36 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.36 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.36 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.36 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.36 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.36 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.36 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.36 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.36 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.36 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.97/1.36 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.97/1.36 hAPP( Z, Y ) ) }.
% 0.97/1.36 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.97/1.36 ( X, Y ), Z = Y }.
% 0.97/1.36 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.97/1.36 ( X, Y ) }.
% 0.97/1.36 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.36 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.97/1.36 ) ) }.
% 0.97/1.36 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.36 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol22( T, U, W ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol22( X, Y,
% 0.97/1.36 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, T ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol22( X, Y,
% 0.97/1.36 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, T, Z ) }.
% 0.97/1.36 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.36 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol23( Z, Y
% 0.97/1.36 ), Y ) }.
% 0.97/1.36 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.36 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.36 skol23( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.97/1.36 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.36 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.97/1.36 , skol23( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.36 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.36 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.36 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.97/1.36 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.97/1.36 .
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.36 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.36 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.97/1.36 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol24( T, U, W ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol24( X, Y,
% 0.97/1.36 Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, T ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol24( X, Y,
% 0.97/1.36 Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, T, Z ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.97/1.36 ), c_Orderings_Oord__class_Oless__eq( X, T, skol25( X, U, W, T ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.97/1.36 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.97/1.36 ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.97/1.36 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.97/1.36 hAPP( Z, T ), hAPP( Z, skol25( X, Y, Z, T ) ) ) ),
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.97/1.36 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.97/1.36 ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, skol26( X, Y ) ) ), X ) ) }.
% 0.97/1.36 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.97/1.36 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.36 tc_Nat_Onat, skol27( X, Y ), skol58( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.97/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.36 hAPP( Y, skol58( X, Y ) ), hAPP( Y, skol27( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.97/1.36 , Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.36 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol28( Z, T ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol28( X, Y ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol59( X, Y, Z ) ) ), Z ),
% 0.97/1.36 c_SEQ_OBseq( X, Y ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.36 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.97/1.36 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.36 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.97/1.36 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.97/1.36 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.97/1.36 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Nat_Onat ) ) = Y }.
% 0.97/1.36 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.36 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.97/1.36 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.97/1.36 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.97/1.36 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.97/1.36 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.36 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.36 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.97/1.36 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.36 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.36 ), X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.36 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.97/1.36 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.97/1.36 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.36 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.97/1.36 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.36 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.36 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.36 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.97/1.36 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.97/1.36 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.36 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.36 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.97/1.36 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.36 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.36 ( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.36 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( X ) }.
% 0.97/1.36 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.36 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.36 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.36 = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.36 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.36 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.97/1.36 ) }.
% 0.97/1.36 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Nat_Onat ) ) = Y }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.36 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.36 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.36 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.97/1.36 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.36 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.36 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.36 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.36 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.36 .
% 0.97/1.36 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.36 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.36 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ) }.
% 0.97/1.36 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.36 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.36 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.97/1.36 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.97/1.36 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.36 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.36 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.36 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.36 ( hAPP( c_Power_Opower__class_Opower( X ),
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) =
% 0.97/1.36 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.36 ), Z ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.97/1.36 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.36 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.36 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.36 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.36 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.36 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.36 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.36 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.36 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.97/1.36 ) ) }.
% 0.97/1.36 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.36 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.36 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.36 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.36 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.36 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.36 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.97/1.36 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.36 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.36 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.36 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.36 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.97/1.36 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( Z, T ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.36 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, skol60( X, Y ) ) ) ),
% 0.97/1.36 skol29( X, Y ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.36 ( Y, skol67( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, T ) ) )
% 0.97/1.36 , Z ), c_SEQ_OBseq( X, Y ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol30( Z, T ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.36 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y, skol61( X, Y ) ) )
% 0.97/1.36 ) ), skol30( X, Y ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.36 ( Y, skol68( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y
% 0.97/1.36 , T ) ) ) ), Z ), c_SEQ_OBseq( X, Y ) }.
% 0.97/1.36 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.97/1.36 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.97/1.36 tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.36 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.36 .
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.36 ( tc_Int_Oint ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.97/1.36 }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Int_Oint ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.97/1.36 }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Int_Oint ) ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Int_Oint ) ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.97/1.36 .
% 0.97/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), X ) = X }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ) ) = X }.
% 0.97/1.36 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.97/1.36 ( tc_Int_Oint ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.97/1.36 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.36 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.97/1.36 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.97/1.36 = X }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Int_Oint ) ) ) }.
% 0.97/1.36 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Int_Oint ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.97/1.36 .
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.36 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.36 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.97/1.36 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.97/1.36 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.36 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.97/1.36 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.97/1.36 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.36 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.36 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ) }.
% 0.97/1.36 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.36 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.97/1.36 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.36 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.97/1.36 tc_Int_Oint, X ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.97/1.36 tc_Int_Oint, X ) = X }.
% 0.97/1.36 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.97/1.36 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.97/1.36 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.97/1.36 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.36 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.97/1.36 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.97/1.36 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.36 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.97/1.36 ( tc_Int_Oint ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.36 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.36 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.36 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.97/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.36 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.36 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.97/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.36 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.36 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.36 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), Y ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.36 ), X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ) ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Int_Oint, X, Y ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.97/1.36 ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol31( X, Y, Z ) ) ), Y ),
% 0.97/1.36 c_SEQ_OBseq( X, Z ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.97/1.36 ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Int_Oint, X, Y ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol32( Z, T ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol32( X, Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol33( Z, Y ) ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.97/1.36 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Int_Oint, skol33( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.36 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.97/1.36 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.97/1.36 , Z ), X ) ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol34( Z, Y ) ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.97/1.36 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.97/1.36 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Int_Oint, skol34( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.36 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.97/1.36 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.97/1.36 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.97/1.36 ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol35( Z, T ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol35( X, Y ) ), X ) =
% 0.97/1.36 Y }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.97/1.36 skol35( X, Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol36( Z, T ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol36( X, Y ) ), X ) =
% 0.97/1.36 Y }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.36 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 0.97/1.36 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.36 ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.36 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! X = Y,
% 0.97/1.36 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.36 ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.36 tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.36 ), c_Transcendental_Oln( Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.97/1.36 ( X ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.36 tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.97/1.36 ( X ), c_Transcendental_Oln( Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.36 ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.36 ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.36 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.36 ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.97/1.36 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! X =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 0.97/1.36 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.36 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.36 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.36 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.36 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.36 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.36 ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.36 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.36 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.36 tc_RealDef_Oreal ), X ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_RealDef_Oreal, c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) )
% 0.97/1.36 }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.97/1.36 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) ), X ) }.
% 0.97/1.36 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 0.97/1.36 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.36 tc_Nat_Onat, skol37( X, Y ), skol62( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.97/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.36 hAPP( Y, skol37( X, Y ) ), hAPP( Y, skol62( X, Y ) ) ), c_SEQ_Oincseq( X
% 0.97/1.36 , Y ) }.
% 0.97/1.36 { alpha37( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.97/1.36 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol38( T, Y, U ), Y ) }
% 0.97/1.36 .
% 0.97/1.36 { alpha37( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.97/1.36 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ), hAPP(
% 0.97/1.36 X, skol38( X, Y, Z ) ) = Z }.
% 0.97/1.36 { ! alpha37( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol39( Z
% 0.97/1.36 , Y ), Y ) }.
% 0.97/1.36 { ! alpha37( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Int_Oint, hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, skol39( X
% 0.97/1.36 , Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, skol39( X,
% 0.97/1.36 Y ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.97/1.36 ( tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Nat_Onat ) ) ), hAPP( X, Z ) ) ), c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Int_Oint ) ), alpha37( X, Y ) }.
% 0.97/1.36 { alpha38( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.97/1.36 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol40( T, Y, U ), Y ) }
% 0.97/1.36 .
% 0.97/1.36 { alpha38( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.97/1.36 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ), hAPP(
% 0.97/1.36 X, skol40( X, Y, Z ) ) = Z }.
% 0.97/1.36 { ! alpha38( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol41( Z
% 0.97/1.36 , Y ), Y ) }.
% 0.97/1.36 { ! alpha38( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Int_Oint, hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, skol41( X
% 0.97/1.36 , Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, skol41( X,
% 0.97/1.36 Y ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.97/1.36 ( tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X,
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Nat_Onat ) ) ), hAPP( X, Z ) ) ), c_Groups_Oone__class_Oone(
% 0.97/1.36 tc_Int_Oint ) ), alpha38( X, Y ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol42( U, W, V0, T )
% 0.97/1.36 ), c_SEQ_OBseq( X, Y ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol42( X, Y, Z, T ) ) ), Z
% 0.97/1.36 ), c_SEQ_OBseq( X, Y ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol43( X, Y, Z ) ) ), Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, c_Nat_OSuc( skol63( X, Y ) ) ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol69( X, Y, Z ) ) ),
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol71( T, U ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol69( X, Y, Z ) ) ),
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol71( X, Y ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol44( X, Y, Z ) ) ), Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, c_Nat_OSuc( skol64( X, Y ) ) ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol70( X, Y, Z ) ) ),
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol72( T, U ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol70( X, Y, Z ) ) ),
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol72( X, Y ) ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.36 X ) ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol45( X, Y ) ) ) }.
% 0.97/1.36 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.97/1.36 .
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.36 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.97/1.36 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.97/1.36 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.36 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.36 ), X ) ) }.
% 0.97/1.36 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha7( X, Y ), alpha19
% 0.97/1.36 ( X, Y ) }.
% 0.97/1.36 { ! alpha7( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.36 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! alpha19( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.36 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! alpha19( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! alpha19( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha19( X, Y ) }.
% 0.97/1.36 { ! alpha7( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! alpha7( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.97/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha8( X, Y ), alpha20( X
% 0.97/1.36 , Y ) }.
% 0.97/1.36 { ! alpha8( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.36 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! alpha20( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.36 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! alpha20( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! alpha20( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha20( X, Y ) }.
% 0.97/1.36 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.97/1.36 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.36 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.36 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.97/1.36 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.36 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.36 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.36 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.36 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.97/1.36 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.36 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.97/1.36 .
% 0.97/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.36 ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.36 , c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.97/1.36 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.97/1.36 }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.97/1.36 c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.36 ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.36 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.97/1.36 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.36 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.36 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.36 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.97/1.36 { ! c_Nat_OSuc( X ) = X }.
% 0.97/1.36 { ! X = c_Nat_OSuc( X ) }.
% 0.97/1.36 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.97/1.36 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.97/1.36 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.36 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.36 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.97/1.36 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.36 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.36 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.97/1.36 }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.36 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.36 X ) ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.97/1.36 .
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.97/1.36 .
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.97/1.36 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.36 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 0.97/1.36 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.36 c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! alpha9( X, Y ), Y = c_Nat_OSuc( skol46( Z, Y ) ) }.
% 0.97/1.36 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol46( X,
% 0.97/1.36 Y ), X ) }.
% 0.97/1.36 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.36 ), alpha9( X, Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol47( X ) ) }.
% 0.97/1.36 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.36 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.36 ), X ) ) }.
% 0.97/1.36 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.36 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.97/1.36 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.36 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.97/1.36 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.36 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.97/1.36 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.97/1.36 ) ) }.
% 0.97/1.36 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.36 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.36 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.36 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.36 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.36 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.36 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.97/1.36 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.36 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.36 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.36 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.97/1.36 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.97/1.36 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.36 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.36 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 X ), Y ), Z = Y }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.36 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.97/1.36 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.36 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.36 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.97/1.36 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.36 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.36 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.36 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.97/1.36 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.97/1.36 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.97/1.36 ) ) = X }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.36 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.97/1.36 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.36 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.36 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.97/1.36 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.97/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.36 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.97/1.36 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.36 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.36 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.97/1.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.97/1.36 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.97/1.36 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.36 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, c_Nat_OSuc( skol48( X, Y ) ) ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol65( X, Y, Z ) ) ),
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.97/1.36 .
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, c_Nat_OSuc( skol49( X, Y ) ) ) ) }.
% 0.97/1.36 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol66( X, Y, Z ) ) ),
% 0.97/1.36 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.97/1.36 .
% 0.97/1.36 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.97/1.36 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.36 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, skol50( X, Y ) ) ), X ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.36 tc_Nat_Onat, c_Nat_OSuc( skol50( X, Y ) ) ) ), X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.97/1.36 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.97/1.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.97/1.36 }.
% 0.97/1.36 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.36 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.36 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.97/1.36 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.36 ( tc_Int_Oint, Y ), X ) }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.36 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.97/1.36 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.36 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.97/1.36 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.36 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.97/1.36 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 }.
% 0.97/1.36 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha10( X, Y ) }.
% 0.97/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.36 { ! alpha10( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.36 { ! alpha10( X, Y ), alpha21( X, Y ), alpha24( X, Y ) }.
% 0.97/1.36 { ! alpha21( X, Y ), alpha10( X, Y ) }.
% 0.97/1.36 { ! alpha24( X, Y ), alpha10( X, Y ) }.
% 0.97/1.36 { ! alpha24( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! alpha24( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha24( X, Y ) }.
% 0.97/1.36 { ! alpha21( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.36 { ! alpha21( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha21( X, Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.97/1.36 , Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.97/1.36 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.36 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.97/1.36 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.36 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.36 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, X, Y ), X ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.97/1.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, Z, Y ), X ) }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.97/1.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.97/1.36 ) }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.97/1.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.97/1.36 ) }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.97/1.36 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.97/1.36 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.36 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.36 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.97/1.36 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.97/1.36 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.36 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.36 alpha11( X, Z ) }.
% 0.97/1.36 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.36 alpha22( X, Y, Z ) }.
% 0.97/1.36 { ! alpha11( X, Z ), ! alpha22( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.36 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.36 { ! alpha22( X, Y, Z ), alpha25( X, Y, Z ) }.
% 0.97/1.36 { ! alpha22( X, Y, Z ), alpha27( X, Y, Z ) }.
% 0.97/1.36 { ! alpha25( X, Y, Z ), ! alpha27( X, Y, Z ), alpha22( X, Y, Z ) }.
% 0.97/1.36 { ! alpha27( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha30( X, Y, Z ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha27( X, Y, Z ) }.
% 0.97/1.36 { ! alpha30( X, Y, Z ), alpha27( X, Y, Z ) }.
% 0.97/1.36 { ! alpha30( X, Y, Z ), ! alpha32( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.36 { ! hBOOL( hAPP( Z, skol51( T, U, Z ) ) ), alpha30( X, Y, Z ) }.
% 0.97/1.36 { alpha32( X, Y, skol51( X, Y, Z ) ), alpha30( X, Y, Z ) }.
% 0.97/1.36 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.36 skol52( X, T, U ) ) }.
% 0.97/1.36 { ! alpha32( X, Y, Z ), alpha34( X, Y, Z, skol52( X, Y, Z ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha34( X, Y, Z
% 0.97/1.36 , T ), alpha32( X, Y, Z ) }.
% 0.97/1.36 { ! alpha34( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.36 { ! alpha34( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.97/1.36 .
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha34( X,
% 0.97/1.36 Y, Z, T ) }.
% 0.97/1.36 { ! alpha25( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha28( X, Y, Z ) }.
% 0.97/1.36 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.36 tc_Int_Oint ), X ), alpha25( X, Y, Z ) }.
% 0.97/1.36 { ! alpha28( X, Y, Z ), alpha25( X, Y, Z ) }.
% 0.97/1.36 { ! alpha28( X, Y, Z ), ! alpha31( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.36 { ! hBOOL( hAPP( Z, skol53( T, U, Z ) ) ), alpha28( X, Y, Z ) }.
% 0.97/1.36 { alpha31( X, Y, skol53( X, Y, Z ) ), alpha28( X, Y, Z ) }.
% 0.97/1.36 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol54( T, U, W ) ) }.
% 0.97/1.36 { ! alpha31( X, Y, Z ), alpha33( X, Y, Z, skol54( X, Y, Z ) ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha33( X, Y, Z, T )
% 0.97/1.36 , alpha31( X, Y, Z ) }.
% 0.97/1.36 { ! alpha33( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.97/1.36 ) }.
% 0.97/1.36 { ! alpha33( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.97/1.36 .
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.97/1.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha33( X,
% 0.97/1.36 Y, Z, T ) }.
% 0.97/1.36 { ! alpha11( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.36 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.36 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha11( X, Y ) }.
% 0.97/1.36 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha11
% 0.97/1.36 ( X, Y ) }.
% 0.97/1.36 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha39( X,
% 0.97/1.36 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, T, Z ) = Y }.
% 0.97/1.36 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha39( X,
% 0.97/1.36 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.36 tc_Int_Oint, T, Z ) = Y }.
% 0.97/1.36 { ! alpha39( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.36 { ! alpha39( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.36 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha39( X, Y ) }.
% 0.97/1.36 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.37 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.97/1.37 , alpha39( X, Y ) }.
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.37 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) }.
% 0.97/1.37 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.37 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.97/1.37 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.97/1.37 ( tc_Int_Oint, X, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }
% 0.97/1.37 .
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.37 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.37 tc_Nat_Onat, skol55( X ) ), X ) }.
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.37 tc_Nat_Onat, c_Nat_OSuc( skol55( X ) ) ) ) }.
% 0.97/1.37 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.97/1.37 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.37 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.97/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.97/1.37 tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.97/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.37 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.97/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.37 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.97/1.37 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.97/1.37 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.97/1.37 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.97/1.37 ( X ), T, Z ), Y ) }.
% 0.97/1.37 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.97/1.37 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.37 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.37 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.97/1.37 ( X ), Z, Y ) ) }.
% 0.97/1.37 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.97/1.37 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.97/1.37 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.37 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.97/1.37 ( X ), Z, Y ) ) }.
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.37 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.97/1.37 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.37 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.37 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.37 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.37 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.37 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.37 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.97/1.37 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.97/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.97/1.37 tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.37 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.37 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.97/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.37 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.37 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.37 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.37 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.37 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.37 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.37 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.37 alpha12( X, Z ) }.
% 0.97/1.37 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.37 alpha23( X, Y, Z ) }.
% 0.97/1.37 { ! alpha12( X, Z ), ! alpha23( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.37 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.37 { ! alpha23( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.37 alpha26( X, Y, Z ) }.
% 0.97/1.37 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha23( X, Y, Z ) }.
% 0.97/1.37 { ! alpha26( X, Y, Z ), alpha23( X, Y, Z ) }.
% 0.97/1.37 { ! alpha26( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.97/1.37 ), alpha29( X, Y, Z, T ) }.
% 0.97/1.37 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol56( X, T, U ), X ),
% 0.97/1.37 alpha26( X, Y, Z ) }.
% 0.97/1.37 { ! alpha29( X, Y, Z, skol56( X, Y, Z ) ), alpha26( X, Y, Z ) }.
% 0.97/1.37 { ! alpha29( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.37 hBOOL( hAPP( Z, U ) ) }.
% 0.97/1.37 { ! hBOOL( hAPP( Z, skol57( U, W, Z, V0 ) ) ), alpha29( X, Y, Z, T ) }.
% 0.97/1.37 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol57( X, Y, Z, T ) )
% 0.97/1.37 , T ), alpha29( X, Y, Z, T ) }.
% 0.97/1.37 { ! alpha12( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.37 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.37 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha12( X, Y ) }.
% 0.97/1.37 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12
% 0.97/1.37 ( X, Y ) }.
% 0.97/1.37 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.37 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.37 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.97/1.37 ( tc_fun( Y, X ) ) }.
% 0.97/1.37 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.97/1.37 ) ) }.
% 0.97/1.37 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.97/1.37 .
% 0.97/1.37 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.97/1.37 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.97/1.37 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.97/1.37 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.37 tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.97/1.37 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.97/1.37 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.97/1.37 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.97/1.37 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.97/1.37 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.97/1.37 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.97/1.37 { class_Power_Opower( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.97/1.37 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.97/1.37 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.97/1.37 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.37 tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.97/1.37 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.97/1.37 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.97/1.37 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.97/1.37 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.97/1.37 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.97/1.37 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.97/1.37 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.37 tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.97/1.37 .
% 0.97/1.37 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Oabs__if( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.37 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.37 tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.37 { ! class_Rings_Oidom( X ),
% 0.97/1.37 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.97/1.37 ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.97/1.37 X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.97/1.37 ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.97/1.37 }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 0.97/1.37 .
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.37 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.37 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.37 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.97/1.37 ( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.97/1.37 ( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Olinordered__idom( X ), class_Groups_Oabs__if(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.97/1.37 }.
% 0.97/1.37 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.97/1.37 ) ) }.
% 0.97/1.37 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.97/1.37 .
% 0.97/1.37 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.97/1.37 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.97/1.37 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm(
% 0.97/1.37 tc_Complex_Ocomplex, v_c____ ) ), c_Groups_Oabs__class_Oabs(
% 0.97/1.37 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.37 tc_RealDef_Oreal ), v_r ), v_m____ ) ) ) ) }.
% 0.97/1.37
% 0.97/1.37 *** allocated 15000 integers for clauses
% 0.97/1.37 *** allocated 22500 integers for clauses
% 0.97/1.37 *** allocated 33750 integers for clauses
% 0.97/1.37 *** allocated 50625 integers for clauses
% 0.97/1.37 *** allocated 75937 integers for clauses
% 0.97/1.37 percentage equality = 0.242223, percentage horn = 0.912150
% 0.97/1.37 This is a problem with some equality
% 0.97/1.37
% 0.97/1.37
% 0.97/1.37
% 0.97/1.37 Options Used:
% 0.97/1.37
% 0.97/1.37 useres = 1
% 0.97/1.37 useparamod = 1
% 0.97/1.37 useeqrefl = 1
% 0.97/1.37 useeqfact = 1
% 0.97/1.37 usefactor = 1
% 0.97/1.37 usesimpsplitting = 0
% 0.97/1.37 usesimpdemod = 5
% 0.97/1.37 usesimpres = 3
% 0.97/1.37
% 0.97/1.37 resimpinuse = 1000
% 0.97/1.37 resimpclauses = 20000
% 0.97/1.37 substype = eqrewr
% 0.97/1.37 backwardsubs = 1
% 0.97/1.37 selectoldest = 5
% 0.97/1.37
% 0.97/1.37 litorderings [0] = split
% 0.97/1.37 litorderings [1] = extend the termordering, first sorting on arguments
% 0.97/1.37
% 0.97/1.37 termordering = kbo
% 0.97/1.37
% 0.97/1.37 litapriori = 0
% 0.97/1.37 termapriori = 1
% 0.97/1.37 litaposteriori = 0
% 0.97/1.37 termaposteriori = 0
% 0.97/1.37 demodaposteriori = 0
% 0.97/1.37 ordereqreflfact = 0
% 0.97/1.37
% 0.97/1.37 litselect = negord
% 0.97/1.37
% 0.97/1.37 maxweight = 15
% 0.97/1.37 maxdepth = 30000
% 0.97/1.37 maxlength = 115
% 0.97/1.37 maxnrvars = 195
% 0.97/1.37 excuselevel = 1
% 0.97/1.37 increasemaxweight = 1
% 0.97/1.37
% 0.97/1.37 maxselected = 10000000
% 0.97/1.37 maxnrclauses = 10000000
% 0.97/1.37
% 0.97/1.37 showgenerated = 0
% 0.97/1.37 showkept = 0
% 0.97/1.37 showselected = 0
% 0.97/1.37 showdeleted = 0
% 0.97/1.37 showresimp = 1
% 0.97/1.37 showstatus = 2000
% 0.97/1.37
% 0.97/1.37 prologoutput = 0
% 0.97/1.37 nrgoals = 5000000
% 0.97/1.37 totalproof = 1
% 0.97/1.37
% 0.97/1.37 Symbols occurring in the translation:
% 0.97/1.37
% 0.97/1.37 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.97/1.37 . [1, 2] (w:1, o:202, a:1, s:1, b:0),
% 0.97/1.37 ! [4, 1] (w:0, o:111, a:1, s:1, b:0),
% 0.97/1.37 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.37 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.37 hAPP [38, 2] (w:1, o:226, a:1, s:1, b:0),
% 0.97/1.37 tc_RealDef_Oreal [39, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.97/1.37 c_Groups_Ozero__class_Ozero [40, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.97/1.37 tc_Complex_Ocomplex [41, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.97/1.37 v_c____ [42, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.97/1.37 c_RealVector_Onorm__class_Onorm [43, 2] (w:1, o:227, a:1, s:1, b:0),
% 0.97/1.37
% 0.97/1.37 c_Orderings_Oord__class_Oless__eq [44, 3] (w:1, o:291, a:1, s:1, b:0)
% 0.97/1.37 ,
% 0.97/1.37 c_Groups_Otimes__class_Otimes [45, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.97/1.37 v_r [46, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.97/1.37 v_m____ [47, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.97/1.37 c_Groups_Oabs__class_Oabs [48, 2] (w:1, o:228, a:1, s:1, b:0),
% 0.97/1.37 c_Groups_Oone__class_Oone [50, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.97/1.37 c_Groups_Oplus__class_Oplus [51, 3] (w:1, o:292, a:1, s:1, b:0),
% 0.97/1.37 c_Orderings_Oord__class_Oless [52, 3] (w:1, o:293, a:1, s:1, b:0),
% 0.97/1.37 class_RealVector_Oreal__normed__vector [57, 1] (w:1, o:119, a:1, s:1
% 0.97/1.37 , b:0),
% 0.97/1.37 class_RealVector_Oreal__normed__algebra [58, 1] (w:1, o:120, a:1, s:1
% 0.97/1.37 , b:0),
% 0.97/1.37 class_Rings_Olinordered__semidom [60, 1] (w:1, o:123, a:1, s:1, b:0)
% 0.97/1.37 ,
% 0.97/1.37 class_Rings_Olinordered__ring [61, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Olinordered__ring__strict [63, 1] (w:1, o:122, a:1, s:1
% 0.97/1.37 , b:0),
% 0.97/1.37 class_RealVector_Oreal__normed__algebra__1 [64, 1] (w:1, o:124, a:1
% 0.97/1.37 , s:1, b:0),
% 0.97/1.37 class_Rings_Oordered__cancel__semiring [72, 1] (w:1, o:128, a:1, s:1
% 0.97/1.37 , b:0),
% 0.97/1.37 class_Rings_Oordered__ring [73, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Oordered__semiring [76, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Oordered__comm__semiring [77, 1] (w:1, o:132, a:1, s:1
% 0.97/1.37 , b:0),
% 0.97/1.37 class_Rings_Olinordered__semiring__strict [80, 1] (w:1, o:133, a:1
% 0.97/1.37 , s:1, b:0),
% 0.97/1.37 class_Rings_Olinordered__semiring [81, 1] (w:1, o:134, a:1, s:1, b:0)
% 0.97/1.37 ,
% 0.97/1.37 class_Rings_Olinordered__idom [83, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Oordered__ring__abs [84, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.97/1.37
% 0.97/1.37 class_Rings_Olinordered__semiring__1 [88, 1] (w:1, o:136, a:1, s:1
% 0.97/1.37 , b:0),
% 0.97/1.37 class_Rings_Olinordered__semiring__1__strict [92, 1] (w:1, o:137, a:1
% 0.97/1.37 , s:1, b:0),
% 0.97/1.37 class_Rings_Ono__zero__divisors [93, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.97/1.37
% 0.97/1.37 class_Rings_Oring__no__zero__divisors [94, 1] (w:1, o:138, a:1, s:1
% 0.97/1.37 , b:0),
% 0.97/1.37 class_Rings_Omult__zero [95, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Ozero__neq__one [96, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Osemiring [98, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Ocomm__semiring [101, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Olinordered__comm__semiring__strict [104, 1] (w:1, o:125
% 0.97/1.37 , a:1, s:1, b:0),
% 0.97/1.37 class_RealVector_Oreal__normed__div__algebra [107, 1] (w:1, o:147, a:
% 0.97/1.37 1, s:1, b:0),
% 0.97/1.37 v_cs____ [109, 0] (w:1, o:81, a:1, s:1, b:0),
% 0.97/1.37 c_Polynomial_Opoly [110, 2] (w:1, o:229, a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Oordered__comm__monoid__add [111, 1] (w:1, o:151, a:1
% 0.97/1.37 , s:1, b:0),
% 0.97/1.37 class_Groups_Oordered__ab__group__add__abs [112, 1] (w:1, o:152, a:1
% 0.97/1.37 , s:1, b:0),
% 0.97/1.37 class_Groups_Ozero [114, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Oab__semigroup__mult [115, 1] (w:1, o:154, a:1, s:1, b:0
% 0.97/1.37 ),
% 0.97/1.37 class_Groups_Oab__semigroup__add [116, 1] (w:1, o:155, a:1, s:1, b:0)
% 0.97/1.37 ,
% 0.97/1.37 class_Groups_Ocancel__semigroup__add [117, 1] (w:1, o:156, a:1, s:1
% 0.97/1.37 , b:0),
% 0.97/1.37 class_Groups_Ocancel__ab__semigroup__add [118, 1] (w:1, o:157, a:1
% 0.97/1.37 , s:1, b:0),
% 0.97/1.37 class_Groups_Oone [119, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Omonoid__add [120, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Ocomm__monoid__add [121, 1] (w:1, o:161, a:1, s:1, b:0)
% 0.97/1.37 ,
% 0.97/1.37 class_Groups_Olinordered__ab__group__add [122, 1] (w:1, o:159, a:1
% 0.97/1.37 , s:1, b:0),
% 0.97/1.37 class_Groups_Oordered__ab__semigroup__add__imp__le [123, 1] (w:1, o:
% 0.97/1.37 162, a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Oordered__ab__semigroup__add [124, 1] (w:1, o:163, a:1
% 0.97/1.37 , s:1, b:0),
% 0.97/1.37 class_Groups_Oordered__cancel__ab__semigroup__add [125, 1] (w:1, o:
% 0.97/1.37 164, a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Omonoid__mult [126, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Ocomm__monoid__mult [127, 1] (w:1, o:166, a:1, s:1, b:0)
% 0.97/1.37 ,
% 0.97/1.37 class_Rings_Ocomm__semiring__1 [128, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.97/1.37
% 0.97/1.37 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.97/1.37 129, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.97/1.37 class_Orderings_Opreorder [130, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.97/1.37 tc_Polynomial_Opoly [131, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Ocomm__semiring__0 [134, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.97/1.37
% 0.97/1.37 class_Orderings_Oord [136, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.97/1.37 tc_fun [137, 2] (w:1, o:266, a:1, s:1, b:0),
% 0.97/1.37 class_Orderings_Olinorder [138, 1] (w:1, o:182, a:1, s:1, b:0),
% 0.97/1.37 class_Orderings_Oorder [139, 1] (w:1, o:173, a:1, s:1, b:0),
% 0.97/1.37 class_Int_Oring__char__0 [146, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Oidom [147, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.97/1.37 c_Polynomial_Oorder [153, 3] (w:1, o:294, a:1, s:1, b:0),
% 0.97/1.37 tc_Nat_Onat [154, 0] (w:1, o:88, a:1, s:1, b:0),
% 0.97/1.37 c_Groups_Osgn__class_Osgn [155, 2] (w:1, o:267, a:1, s:1, b:0),
% 0.97/1.37 c_Polynomial_Opoly__rec [156, 5] (w:1, o:352, a:1, s:1, b:0),
% 0.97/1.37 class_Fields_Olinordered__field__inverse__zero [157, 1] (w:1, o:148
% 0.97/1.37 , a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Osgn__if [158, 1] (w:1, o:184, a:1, s:1, b:0),
% 0.97/1.37 class_Fields_Olinordered__field [159, 1] (w:1, o:149, a:1, s:1, b:0)
% 0.97/1.37 ,
% 0.97/1.37 c_Polynomial_Ocoeff [161, 2] (w:1, o:268, a:1, s:1, b:0),
% 0.97/1.37 c_Groups_Ominus__class_Ominus [162, 3] (w:1, o:295, a:1, s:1, b:0),
% 0.97/1.37 c_Groups_Ouminus__class_Ouminus [163, 2] (w:1, o:269, a:1, s:1, b:0)
% 0.97/1.37 ,
% 0.97/1.37 hBOOL [165, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Oab__group__add [167, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Ogroup__add [171, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Ocomm__ring__1 [176, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Ocomm__ring [177, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Oordered__ab__group__add [181, 1] (w:1, o:188, a:1, s:1
% 0.97/1.37 , b:0),
% 0.97/1.37 class_Rings_Oring [182, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Oring__1__no__zero__divisors [184, 1] (w:1, o:141, a:1
% 0.97/1.37 , s:1, b:0),
% 0.97/1.37 class_Rings_Oring__1 [186, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Oabs__if [187, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.97/1.37 c_RComplete_Onatceiling [189, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.97/1.37 c_RComplete_Onatfloor [190, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.97/1.37 c_RealDef_Oreal [191, 2] (w:1, o:270, a:1, s:1, b:0),
% 0.97/1.37 class_Lattices_Oboolean__algebra [192, 1] (w:1, o:193, a:1, s:1, b:0)
% 0.97/1.37 ,
% 0.97/1.37 class_Lattices_Oab__semigroup__idem__mult [193, 1] (w:1, o:192, a:1
% 0.97/1.37 , s:1, b:0),
% 0.97/1.37 class_Groups_Ominus [196, 1] (w:1, o:194, a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Ouminus [197, 1] (w:1, o:195, a:1, s:1, b:0),
% 0.97/1.37 c_Polynomial_Opos__poly [200, 2] (w:1, o:271, a:1, s:1, b:0),
% 0.97/1.37 c_SEQ_Odecseq [203, 2] (w:1, o:272, a:1, s:1, b:0),
% 0.97/1.37 c_Power_Opower__class_Opower [204, 1] (w:1, o:196, a:1, s:1, b:0),
% 0.97/1.37 c_SEQ_OBseq [205, 2] (w:1, o:273, a:1, s:1, b:0),
% 0.97/1.37 class_Power_Opower [206, 1] (w:1, o:197, a:1, s:1, b:0),
% 0.97/1.37 tc_Int_Oint [207, 0] (w:1, o:102, a:1, s:1, b:0),
% 0.97/1.37 class_Rings_Osemiring__0 [208, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.97/1.37 c_Power_Opower_Opower [211, 3] (w:1, o:296, a:1, s:1, b:0),
% 0.97/1.37 c_Nat__Transfer_Otsub [218, 2] (w:1, o:274, a:1, s:1, b:0),
% 0.97/1.37 c_Transcendental_Oln [221, 1] (w:1, o:198, a:1, s:1, b:0),
% 0.97/1.37 c_SEQ_Oincseq [222, 2] (w:1, o:275, a:1, s:1, b:0),
% 0.97/1.37 c_Nat_OSuc [224, 1] (w:1, o:199, a:1, s:1, b:0),
% 0.97/1.37 c_Divides_Odiv__class_Odiv [230, 3] (w:1, o:297, a:1, s:1, b:0),
% 0.97/1.37 class_Divides_Osemiring__div [231, 1] (w:1, o:200, a:1, s:1, b:0),
% 0.97/1.37 c_SMT_Oz3div [235, 2] (w:1, o:276, a:1, s:1, b:0),
% 0.97/1.37 class_Fields_Ofield [236, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.97/1.37 class_Groups_Ocancel__comm__monoid__add [238, 1] (w:1, o:201, a:1, s:
% 0.97/1.37 1, b:0),
% 0.97/1.37 tc_HOL_Obool [240, 0] (w:1, o:101, a:1, s:1, b:0),
% 2.56/2.96 alpha1 [241, 3] (w:1, o:298, a:1, s:1, b:1),
% 2.56/2.96 alpha2 [242, 3] (w:1, o:303, a:1, s:1, b:1),
% 2.56/2.96 alpha3 [243, 4] (w:1, o:341, a:1, s:1, b:1),
% 2.56/2.96 alpha4 [244, 4] (w:1, o:344, a:1, s:1, b:1),
% 2.56/2.96 alpha5 [245, 3] (w:1, o:305, a:1, s:1, b:1),
% 2.56/2.96 alpha6 [246, 3] (w:1, o:306, a:1, s:1, b:1),
% 2.56/2.96 alpha7 [247, 2] (w:1, o:277, a:1, s:1, b:1),
% 2.56/2.96 alpha8 [248, 2] (w:1, o:278, a:1, s:1, b:1),
% 2.56/2.96 alpha9 [249, 2] (w:1, o:279, a:1, s:1, b:1),
% 2.56/2.96 alpha10 [250, 2] (w:1, o:280, a:1, s:1, b:1),
% 2.56/2.96 alpha11 [251, 2] (w:1, o:281, a:1, s:1, b:1),
% 2.56/2.96 alpha12 [252, 2] (w:1, o:282, a:1, s:1, b:1),
% 2.56/2.96 alpha13 [253, 3] (w:1, o:299, a:1, s:1, b:1),
% 2.56/2.96 alpha14 [254, 3] (w:1, o:300, a:1, s:1, b:1),
% 2.56/2.96 alpha15 [255, 4] (w:1, o:345, a:1, s:1, b:1),
% 2.56/2.96 alpha16 [256, 4] (w:1, o:346, a:1, s:1, b:1),
% 2.56/2.96 alpha17 [257, 3] (w:1, o:301, a:1, s:1, b:1),
% 2.56/2.96 alpha18 [258, 3] (w:1, o:302, a:1, s:1, b:1),
% 2.56/2.96 alpha19 [259, 2] (w:1, o:283, a:1, s:1, b:1),
% 2.56/2.96 alpha20 [260, 2] (w:1, o:284, a:1, s:1, b:1),
% 2.56/2.96 alpha21 [261, 2] (w:1, o:285, a:1, s:1, b:1),
% 2.56/2.96 alpha22 [262, 3] (w:1, o:307, a:1, s:1, b:1),
% 2.56/2.96 alpha23 [263, 3] (w:1, o:308, a:1, s:1, b:1),
% 2.56/2.96 alpha24 [264, 2] (w:1, o:286, a:1, s:1, b:1),
% 2.56/2.96 alpha25 [265, 3] (w:1, o:309, a:1, s:1, b:1),
% 2.56/2.96 alpha26 [266, 3] (w:1, o:310, a:1, s:1, b:1),
% 2.56/2.96 alpha27 [267, 3] (w:1, o:311, a:1, s:1, b:1),
% 2.56/2.96 alpha28 [268, 3] (w:1, o:312, a:1, s:1, b:1),
% 2.56/2.96 alpha29 [269, 4] (w:1, o:340, a:1, s:1, b:1),
% 2.56/2.96 alpha30 [270, 3] (w:1, o:313, a:1, s:1, b:1),
% 2.56/2.96 alpha31 [271, 3] (w:1, o:314, a:1, s:1, b:1),
% 2.56/2.96 alpha32 [272, 3] (w:1, o:315, a:1, s:1, b:1),
% 2.56/2.96 alpha33 [273, 4] (w:1, o:342, a:1, s:1, b:1),
% 2.56/2.96 alpha34 [274, 4] (w:1, o:343, a:1, s:1, b:1),
% 2.56/2.96 alpha35 [275, 2] (w:1, o:287, a:1, s:1, b:1),
% 2.56/2.96 alpha36 [276, 3] (w:1, o:316, a:1, s:1, b:1),
% 2.56/2.96 alpha37 [277, 2] (w:1, o:288, a:1, s:1, b:1),
% 2.56/2.96 alpha38 [278, 2] (w:1, o:289, a:1, s:1, b:1),
% 2.56/2.96 alpha39 [279, 2] (w:1, o:290, a:1, s:1, b:1),
% 2.56/2.96 alpha40 [280, 3] (w:1, o:304, a:1, s:1, b:1),
% 2.56/2.96 skol1 [281, 2] (w:1, o:230, a:1, s:1, b:1),
% 2.56/2.96 skol2 [282, 0] (w:1, o:12, a:1, s:1, b:1),
% 2.56/2.96 skol3 [283, 0] (w:1, o:13, a:1, s:1, b:1),
% 2.56/2.96 skol4 [284, 3] (w:1, o:319, a:1, s:1, b:1),
% 2.56/2.96 skol5 [285, 2] (w:1, o:236, a:1, s:1, b:1),
% 2.56/2.96 skol6 [286, 2] (w:1, o:239, a:1, s:1, b:1),
% 2.56/2.96 skol7 [287, 1] (w:1, o:175, a:1, s:1, b:1),
% 2.56/2.96 skol8 [288, 2] (w:1, o:242, a:1, s:1, b:1),
% 2.56/2.96 skol9 [289, 2] (w:1, o:243, a:1, s:1, b:1),
% 2.56/2.96 skol10 [290, 1] (w:1, o:176, a:1, s:1, b:1),
% 2.56/2.96 skol11 [291, 2] (w:1, o:244, a:1, s:1, b:1),
% 2.56/2.96 skol12 [292, 1] (w:1, o:177, a:1, s:1, b:1),
% 2.56/2.96 skol13 [293, 2] (w:1, o:245, a:1, s:1, b:1),
% 2.56/2.96 skol14 [294, 3] (w:1, o:320, a:1, s:1, b:1),
% 2.56/2.96 skol15 [295, 3] (w:1, o:321, a:1, s:1, b:1),
% 2.56/2.96 skol16 [296, 3] (w:1, o:322, a:1, s:1, b:1),
% 2.56/2.96 skol17 [297, 3] (w:1, o:323, a:1, s:1, b:1),
% 2.56/2.96 skol18 [298, 3] (w:1, o:324, a:1, s:1, b:1),
% 2.56/2.96 skol19 [299, 2] (w:1, o:246, a:1, s:1, b:1),
% 2.56/2.96 skol20 [300, 2] (w:1, o:247, a:1, s:1, b:1),
% 2.56/2.96 skol21 [301, 1] (w:1, o:178, a:1, s:1, b:1),
% 2.56/2.96 skol22 [302, 3] (w:1, o:325, a:1, s:1, b:1),
% 2.56/2.96 skol23 [303, 2] (w:1, o:248, a:1, s:1, b:1),
% 2.56/2.96 skol24 [304, 3] (w:1, o:326, a:1, s:1, b:1),
% 2.56/2.96 skol25 [305, 4] (w:1, o:347, a:1, s:1, b:1),
% 2.56/2.96 skol26 [306, 2] (w:1, o:249, a:1, s:1, b:1),
% 2.56/2.96 skol27 [307, 2] (w:1, o:250, a:1, s:1, b:1),
% 2.56/2.96 skol28 [308, 2] (w:1, o:251, a:1, s:1, b:1),
% 2.56/2.96 skol29 [309, 2] (w:1, o:252, a:1, s:1, b:1),
% 2.56/2.96 skol30 [310, 2] (w:1, o:253, a:1, s:1, b:1),
% 2.56/2.96 skol31 [311, 3] (w:1, o:317, a:1, s:1, b:1),
% 2.56/2.96 skol32 [312, 2] (w:1, o:254, a:1, s:1, b:1),
% 2.56/2.96 skol33 [313, 2] (w:1, o:255, a:1, s:1, b:1),
% 2.56/2.96 skol34 [314, 2] (w:1, o:256, a:1, s:1, b:1),
% 2.56/2.96 skol35 [315, 2] (w:1, o:257, a:1, s:1, b:1),
% 2.56/2.96 skol36 [316, 2] (w:1, o:258, a:1, s:1, b:1),
% 2.56/2.96 skol37 [317, 2] (w:1, o:259, a:1, s:1, b:1),
% 2.56/2.96 skol38 [318, 3] (w:1, o:318, a:1, s:1, b:1),
% 2.56/2.96 skol39 [319, 2] (w:1, o:260, a:1, s:1, b:1),
% 17.65/18.05 skol40 [320, 3] (w:1, o:327, a:1, s:1, b:1),
% 17.65/18.05 skol41 [321, 2] (w:1, o:231, a:1, s:1, b:1),
% 17.65/18.05 skol42 [322, 4] (w:1, o:348, a:1, s:1, b:1),
% 17.65/18.05 skol43 [323, 3] (w:1, o:328, a:1, s:1, b:1),
% 17.65/18.05 skol44 [324, 3] (w:1, o:329, a:1, s:1, b:1),
% 17.65/18.05 skol45 [325, 2] (w:1, o:232, a:1, s:1, b:1),
% 17.65/18.05 skol46 [326, 2] (w:1, o:233, a:1, s:1, b:1),
% 17.65/18.05 skol47 [327, 1] (w:1, o:179, a:1, s:1, b:1),
% 17.65/18.05 skol48 [328, 2] (w:1, o:234, a:1, s:1, b:1),
% 17.65/18.05 skol49 [329, 2] (w:1, o:235, a:1, s:1, b:1),
% 17.65/18.05 skol50 [330, 2] (w:1, o:237, a:1, s:1, b:1),
% 17.65/18.05 skol51 [331, 3] (w:1, o:330, a:1, s:1, b:1),
% 17.65/18.05 skol52 [332, 3] (w:1, o:331, a:1, s:1, b:1),
% 17.65/18.05 skol53 [333, 3] (w:1, o:332, a:1, s:1, b:1),
% 17.65/18.05 skol54 [334, 3] (w:1, o:333, a:1, s:1, b:1),
% 17.65/18.05 skol55 [335, 1] (w:1, o:180, a:1, s:1, b:1),
% 17.65/18.05 skol56 [336, 3] (w:1, o:334, a:1, s:1, b:1),
% 17.65/18.05 skol57 [337, 4] (w:1, o:349, a:1, s:1, b:1),
% 17.65/18.05 skol58 [338, 2] (w:1, o:238, a:1, s:1, b:1),
% 17.65/18.06 skol59 [339, 3] (w:1, o:335, a:1, s:1, b:1),
% 17.65/18.06 skol60 [340, 2] (w:1, o:261, a:1, s:1, b:1),
% 17.65/18.06 skol61 [341, 2] (w:1, o:262, a:1, s:1, b:1),
% 17.65/18.06 skol62 [342, 2] (w:1, o:263, a:1, s:1, b:1),
% 17.65/18.06 skol63 [343, 2] (w:1, o:264, a:1, s:1, b:1),
% 17.65/18.06 skol64 [344, 2] (w:1, o:265, a:1, s:1, b:1),
% 17.65/18.06 skol65 [345, 3] (w:1, o:336, a:1, s:1, b:1),
% 17.65/18.06 skol66 [346, 3] (w:1, o:337, a:1, s:1, b:1),
% 17.65/18.06 skol67 [347, 4] (w:1, o:350, a:1, s:1, b:1),
% 17.65/18.06 skol68 [348, 4] (w:1, o:351, a:1, s:1, b:1),
% 17.65/18.06 skol69 [349, 3] (w:1, o:338, a:1, s:1, b:1),
% 17.65/18.06 skol70 [350, 3] (w:1, o:339, a:1, s:1, b:1),
% 17.65/18.06 skol71 [351, 2] (w:1, o:240, a:1, s:1, b:1),
% 17.65/18.06 skol72 [352, 2] (w:1, o:241, a:1, s:1, b:1).
% 17.65/18.06
% 17.65/18.06
% 17.65/18.06 Starting Search:
% 17.65/18.06
% 17.65/18.06 *** allocated 113905 integers for clauses
% 17.65/18.06 *** allocated 170857 integers for clauses
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06
% 17.65/18.06 Intermediate Status:
% 17.65/18.06 Generated: 2932
% 17.65/18.06 Kept: 2022
% 17.65/18.06 Inuse: 42
% 17.65/18.06 Deleted: 4
% 17.65/18.06 Deletedinuse: 0
% 17.65/18.06
% 17.65/18.06 *** allocated 256285 integers for clauses
% 17.65/18.06 *** allocated 170857 integers for termspace/termends
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06
% 17.65/18.06 Intermediate Status:
% 17.65/18.06 Generated: 6972
% 17.65/18.06 Kept: 4117
% 17.65/18.06 Inuse: 126
% 17.65/18.06 Deleted: 5
% 17.65/18.06 Deletedinuse: 0
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06 *** allocated 384427 integers for clauses
% 17.65/18.06 *** allocated 256285 integers for termspace/termends
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06
% 17.65/18.06 Intermediate Status:
% 17.65/18.06 Generated: 13047
% 17.65/18.06 Kept: 6122
% 17.65/18.06 Inuse: 215
% 17.65/18.06 Deleted: 5
% 17.65/18.06 Deletedinuse: 0
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06 *** allocated 576640 integers for clauses
% 17.65/18.06 *** allocated 384427 integers for termspace/termends
% 17.65/18.06
% 17.65/18.06 Intermediate Status:
% 17.65/18.06 Generated: 16871
% 17.65/18.06 Kept: 8202
% 17.65/18.06 Inuse: 311
% 17.65/18.06 Deleted: 5
% 17.65/18.06 Deletedinuse: 0
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06
% 17.65/18.06 Intermediate Status:
% 17.65/18.06 Generated: 22427
% 17.65/18.06 Kept: 10302
% 17.65/18.06 Inuse: 376
% 17.65/18.06 Deleted: 6
% 17.65/18.06 Deletedinuse: 1
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06 *** allocated 576640 integers for termspace/termends
% 17.65/18.06 *** allocated 864960 integers for clauses
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06
% 17.65/18.06 Intermediate Status:
% 17.65/18.06 Generated: 27372
% 17.65/18.06 Kept: 12558
% 17.65/18.06 Inuse: 406
% 17.65/18.06 Deleted: 6
% 17.65/18.06 Deletedinuse: 1
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06
% 17.65/18.06 Intermediate Status:
% 17.65/18.06 Generated: 32990
% 17.65/18.06 Kept: 15223
% 17.65/18.06 Inuse: 459
% 17.65/18.06 Deleted: 8
% 17.65/18.06 Deletedinuse: 1
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06 *** allocated 864960 integers for termspace/termends
% 17.65/18.06
% 17.65/18.06 Intermediate Status:
% 17.65/18.06 Generated: 42860
% 17.65/18.06 Kept: 18054
% 17.65/18.06 Inuse: 503
% 17.65/18.06 Deleted: 9
% 17.65/18.06 Deletedinuse: 1
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06 *** allocated 1297440 integers for clauses
% 17.65/18.06
% 17.65/18.06 Intermediate Status:
% 17.65/18.06 Generated: 51459
% 17.65/18.06 Kept: 20497
% 17.65/18.06 Inuse: 523
% 17.65/18.06 Deleted: 9
% 17.65/18.06 Deletedinuse: 1
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06 Resimplifying clauses:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06
% 17.65/18.06 Intermediate Status:
% 17.65/18.06 Generated: 59901
% 17.65/18.06 Kept: 22626
% 17.65/18.06 Inuse: 538
% 17.65/18.06 Deleted: 401
% 17.65/18.06 Deletedinuse: 3
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06 Resimplifying inuse:
% 17.65/18.06 Done
% 17.65/18.06
% 17.65/18.06
% 17.65/18.06 Intermediate Status:
% 17.65/18.06 Generated: 65501
% 17.65/18.06 Kept: 24626
% 17.65/18.06 Inuse: 590
% 17.65/18.06 Deleted: 401
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 *** allocated 1297440 integers for termspace/termends
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 81821
% 99.29/99.75 Kept: 27427
% 99.29/99.75 Inuse: 603
% 99.29/99.75 Deleted: 401
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 *** allocated 1946160 integers for clauses
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 99368
% 99.29/99.75 Kept: 30233
% 99.29/99.75 Inuse: 613
% 99.29/99.75 Deleted: 401
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 106201
% 99.29/99.75 Kept: 32241
% 99.29/99.75 Inuse: 653
% 99.29/99.75 Deleted: 401
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 112770
% 99.29/99.75 Kept: 34430
% 99.29/99.75 Inuse: 693
% 99.29/99.75 Deleted: 401
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 118380
% 99.29/99.75 Kept: 36509
% 99.29/99.75 Inuse: 748
% 99.29/99.75 Deleted: 401
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 123438
% 99.29/99.75 Kept: 38521
% 99.29/99.75 Inuse: 800
% 99.29/99.75 Deleted: 401
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 *** allocated 1946160 integers for termspace/termends
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 131755
% 99.29/99.75 Kept: 41028
% 99.29/99.75 Inuse: 808
% 99.29/99.75 Deleted: 401
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying clauses:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 *** allocated 2919240 integers for clauses
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 141275
% 99.29/99.75 Kept: 44353
% 99.29/99.75 Inuse: 843
% 99.29/99.75 Deleted: 970
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 150154
% 99.29/99.75 Kept: 46368
% 99.29/99.75 Inuse: 882
% 99.29/99.75 Deleted: 970
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 160969
% 99.29/99.75 Kept: 48419
% 99.29/99.75 Inuse: 898
% 99.29/99.75 Deleted: 970
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 169998
% 99.29/99.75 Kept: 52270
% 99.29/99.75 Inuse: 928
% 99.29/99.75 Deleted: 970
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 181670
% 99.29/99.75 Kept: 55235
% 99.29/99.75 Inuse: 948
% 99.29/99.75 Deleted: 970
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 191348
% 99.29/99.75 Kept: 57491
% 99.29/99.75 Inuse: 958
% 99.29/99.75 Deleted: 970
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 201209
% 99.29/99.75 Kept: 59756
% 99.29/99.75 Inuse: 968
% 99.29/99.75 Deleted: 970
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 208613
% 99.29/99.75 Kept: 62453
% 99.29/99.75 Inuse: 988
% 99.29/99.75 Deleted: 970
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying clauses:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 *** allocated 2919240 integers for termspace/termends
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 216926
% 99.29/99.75 Kept: 64487
% 99.29/99.75 Inuse: 1028
% 99.29/99.75 Deleted: 1060
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 *** allocated 4378860 integers for clauses
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 228226
% 99.29/99.75 Kept: 67355
% 99.29/99.75 Inuse: 1044
% 99.29/99.75 Deleted: 1060
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 234830
% 99.29/99.75 Kept: 69419
% 99.29/99.75 Inuse: 1088
% 99.29/99.75 Deleted: 1060
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 240814
% 99.29/99.75 Kept: 72656
% 99.29/99.75 Inuse: 1103
% 99.29/99.75 Deleted: 1060
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 253201
% 99.29/99.75 Kept: 75612
% 99.29/99.75 Inuse: 1148
% 99.29/99.75 Deleted: 1060
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 263852
% 99.29/99.75 Kept: 77697
% 99.29/99.75 Inuse: 1163
% 99.29/99.75 Deleted: 1060
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 271214
% 99.29/99.75 Kept: 79697
% 99.29/99.75 Inuse: 1206
% 99.29/99.75 Deleted: 1060
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75
% 99.29/99.75 Intermediate Status:
% 99.29/99.75 Generated: 278596
% 99.29/99.75 Kept: 83645
% 99.29/99.75 Inuse: 1223
% 99.29/99.75 Deleted: 1060
% 99.29/99.75 Deletedinuse: 3
% 99.29/99.75
% 99.29/99.75 Resimplifying inuse:
% 99.29/99.75 Done
% 99.29/99.75
% 99.29/99.75 Resimplifying clauses:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 284614
% 238.32/238.78 Kept: 85718
% 238.32/238.78 Inuse: 1248
% 238.32/238.78 Deleted: 1241
% 238.32/238.78 Deletedinuse: 3
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 311988
% 238.32/238.78 Kept: 88505
% 238.32/238.78 Inuse: 1253
% 238.32/238.78 Deleted: 1241
% 238.32/238.78 Deletedinuse: 3
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 319964
% 238.32/238.78 Kept: 90798
% 238.32/238.78 Inuse: 1298
% 238.32/238.78 Deleted: 1241
% 238.32/238.78 Deletedinuse: 3
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 333981
% 238.32/238.78 Kept: 94235
% 238.32/238.78 Inuse: 1323
% 238.32/238.78 Deleted: 1242
% 238.32/238.78 Deletedinuse: 4
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 *** allocated 4378860 integers for termspace/termends
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 351557
% 238.32/238.78 Kept: 98385
% 238.32/238.78 Inuse: 1363
% 238.32/238.78 Deleted: 1242
% 238.32/238.78 Deletedinuse: 4
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 358506
% 238.32/238.78 Kept: 100386
% 238.32/238.78 Inuse: 1408
% 238.32/238.78 Deleted: 1242
% 238.32/238.78 Deletedinuse: 4
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 *** allocated 6568290 integers for clauses
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 368177
% 238.32/238.78 Kept: 102441
% 238.32/238.78 Inuse: 1438
% 238.32/238.78 Deleted: 1242
% 238.32/238.78 Deletedinuse: 4
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 384073
% 238.32/238.78 Kept: 105799
% 238.32/238.78 Inuse: 1463
% 238.32/238.78 Deleted: 1242
% 238.32/238.78 Deletedinuse: 4
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying clauses:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 400363
% 238.32/238.78 Kept: 112333
% 238.32/238.78 Inuse: 1493
% 238.32/238.78 Deleted: 1435
% 238.32/238.78 Deletedinuse: 4
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 411300
% 238.32/238.78 Kept: 117196
% 238.32/238.78 Inuse: 1498
% 238.32/238.78 Deleted: 1435
% 238.32/238.78 Deletedinuse: 4
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 427326
% 238.32/238.78 Kept: 122736
% 238.32/238.78 Inuse: 1548
% 238.32/238.78 Deleted: 1435
% 238.32/238.78 Deletedinuse: 4
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 468451
% 238.32/238.78 Kept: 127403
% 238.32/238.78 Inuse: 1568
% 238.32/238.78 Deleted: 1435
% 238.32/238.78 Deletedinuse: 4
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying clauses:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 480751
% 238.32/238.78 Kept: 129576
% 238.32/238.78 Inuse: 1593
% 238.32/238.78 Deleted: 1631
% 238.32/238.78 Deletedinuse: 4
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 489074
% 238.32/238.78 Kept: 131579
% 238.32/238.78 Inuse: 1621
% 238.32/238.78 Deleted: 1631
% 238.32/238.78 Deletedinuse: 4
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 496059
% 238.32/238.78 Kept: 133743
% 238.32/238.78 Inuse: 1643
% 238.32/238.78 Deleted: 1634
% 238.32/238.78 Deletedinuse: 7
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 504076
% 238.32/238.78 Kept: 136284
% 238.32/238.78 Inuse: 1668
% 238.32/238.78 Deleted: 1637
% 238.32/238.78 Deletedinuse: 10
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 513027
% 238.32/238.78 Kept: 138411
% 238.32/238.78 Inuse: 1698
% 238.32/238.78 Deleted: 1637
% 238.32/238.78 Deletedinuse: 10
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 521861
% 238.32/238.78 Kept: 140549
% 238.32/238.78 Inuse: 1708
% 238.32/238.78 Deleted: 1637
% 238.32/238.78 Deletedinuse: 10
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 *** allocated 6568290 integers for termspace/termends
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 534731
% 238.32/238.78 Kept: 144816
% 238.32/238.78 Inuse: 1728
% 238.32/238.78 Deleted: 1637
% 238.32/238.78 Deletedinuse: 10
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 548937
% 238.32/238.78 Kept: 150667
% 238.32/238.78 Inuse: 1758
% 238.32/238.78 Deleted: 1637
% 238.32/238.78 Deletedinuse: 10
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying clauses:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 *** allocated 9852435 integers for clauses
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 557827
% 238.32/238.78 Kept: 155034
% 238.32/238.78 Inuse: 1768
% 238.32/238.78 Deleted: 1870
% 238.32/238.78 Deletedinuse: 10
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 567885
% 238.32/238.78 Kept: 157034
% 238.32/238.78 Inuse: 1807
% 238.32/238.78 Deleted: 1870
% 238.32/238.78 Deletedinuse: 10
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate Status:
% 238.32/238.78 Generated: 576589
% 238.32/238.78 Kept: 159278
% 238.32/238.78 Inuse: 1838
% 238.32/238.78 Deleted: 1870
% 238.32/238.78 Deletedinuse: 10
% 238.32/238.78
% 238.32/238.78 Resimplifying inuse:
% 238.32/238.78 Done
% 238.32/238.78
% 238.32/238.78
% 238.32/238.78 Intermediate SCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------