TSTP Solution File: SWW180+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW180+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n026.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 300.01s 300.46s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW180+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jun 5 15:25:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.94/1.54 *** allocated 10000 integers for termspace/termends
% 0.94/1.54 *** allocated 10000 integers for clauses
% 0.94/1.54 *** allocated 10000 integers for justifications
% 0.94/1.54 *** allocated 15000 integers for termspace/termends
% 0.94/1.54 *** allocated 22500 integers for termspace/termends
% 0.94/1.54 *** allocated 33750 integers for termspace/termends
% 0.94/1.54 Bliksem 1.12
% 0.94/1.54
% 0.94/1.54
% 0.94/1.54 Automatic Strategy Selection
% 0.94/1.54
% 0.94/1.54 *** allocated 50625 integers for termspace/termends
% 0.94/1.54 *** allocated 75937 integers for termspace/termends
% 0.94/1.54 *** allocated 113905 integers for termspace/termends
% 0.94/1.54
% 0.94/1.54 Clauses:
% 0.94/1.54
% 0.94/1.54 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_z____ ), v_r ) }
% 0.94/1.54 .
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.94/1.54 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.54 ( X, Y ) ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), v_r ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), X ) ), v_m____ ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_r ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.54 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.54 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.94/1.54 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.54 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.94/1.54 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm(
% 0.94/1.54 tc_Complex_Ocomplex, v_c____ ) ), c_Groups_Oabs__class_Oabs(
% 0.94/1.54 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.54 tc_RealDef_Oreal ), v_r ), v_m____ ) ) ) ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.94/1.54 , Y ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), v_z____ ) ), v_m____
% 0.94/1.54 ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_c____ ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), v_z____ ) ) ) ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_c____ ), hAPP(
% 0.94/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), v_r ), v_m____ )
% 0.94/1.54 ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol2 ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), v_r ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), X ) ), skol2 ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.54 Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_RealDef_Oreal ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.94/1.54 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.54 Y ), ! Z = Y }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.54 Z ), ! Z = Y }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.54 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.54 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.94/1.54 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.54 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.54 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.94/1.54 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.54 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.94/1.54 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.54 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.54 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.54 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.94/1.54 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.54 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.54 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.54 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.54 , ! Z = Y }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.54 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.54 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.54 , ! Z = Y }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.54 , ! Y = Z }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.54 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.54 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.94/1.54 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.94/1.54 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.94/1.54 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.54 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.54 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.54 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.54 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.54 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.54 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.54 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.54 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.54 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.54 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.54 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.54 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.94/1.54 ( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.54 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.54 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.54 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.54 , ! Z = Y }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.54 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.54 , T ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.54 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.54 , T, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.54 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.54 , Y, T ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.54 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.54 , T, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, T, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.54 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.54 , Y, Z ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.54 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.54 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.54 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.54 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.54 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.94/1.54 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.94/1.54 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.94/1.54 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.94/1.54 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.54 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.54 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.54 ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.54 ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.94/1.54 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.54 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.94/1.54 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.54 , Y, T ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Z, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Y, Z ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.94/1.54 .
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.94/1.54 .
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.94/1.54 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.54 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.94/1.54 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.94/1.54 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.54 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.94/1.54 hAPP( Y, U ) ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.94/1.54 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.54 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.54 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.94/1.54 hAPP( Y, U ) ) }.
% 0.94/1.54 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.94/1.54 ( X, Z, Y ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.94/1.54 ( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.94/1.54 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.54 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.54 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.94/1.54 hAPP( Y, U ) ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.94/1.54 ( Z, skol3( X, Y, Z ) ), hAPP( Y, skol3( X, Y, Z ) ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.94/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Y, T ), Z = Y }.
% 0.94/1.54 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 T, Y ), Z = Y }.
% 0.94/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 T, Y ), Z = Y }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.54 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.94/1.54 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Y, Z ), T = Y }.
% 0.94/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Y, Z ) }.
% 0.94/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 T, Y ), Z = Y }.
% 0.94/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 T, Y ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.54 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.94/1.54 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.54 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.54 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.94/1.54 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.94/1.54 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.94/1.54 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.54 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.94/1.54 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.54 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.54 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.54 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.54 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.54 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.54 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.54 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.54 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.54 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.54 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.94/1.54 ), U = Z, T = Y }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.94/1.54 ) ), Z ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.54 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.54 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.54 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.94/1.54 ), ! U = T }.
% 0.94/1.54 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.54 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.94/1.54 ), ! Z = Y }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.94/1.54 = Y }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.94/1.54 = Y }.
% 0.94/1.54 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.94/1.54 = Y }.
% 0.94/1.54 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.54 = Y }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.54 = Y }.
% 0.94/1.54 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.54 = Y }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.54 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.94/1.54 ) ) }.
% 0.94/1.54 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.94/1.54 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.94/1.54 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.54 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), v_z____ ) ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_c____ ), hAPP(
% 0.94/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), v_r ), v_m____ )
% 0.94/1.54 ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.94/1.54 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), v_z____ ) ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_c____ ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), hAPP(
% 0.94/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), v_z____ ) ) ) ) ) }
% 0.94/1.54 .
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.94/1.54 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.94/1.54 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.94/1.54 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.94/1.54 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.94/1.54 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.94/1.54 ), Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.94/1.54 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.54 , X ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring__abs( X ), alpha23( X, Z ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring__abs( X ), alpha23( X, Z ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.54 { ! alpha23( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.54 { ! alpha23( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ), alpha23( X, Y ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.54 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.94/1.54 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.94/1.54 .
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.94/1.54 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.94/1.54 }.
% 0.94/1.54 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.54 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.94/1.54 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.54 X, Y, Z ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.94/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.94/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.94/1.54 }.
% 0.94/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.94/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.54 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.54 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.54 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.54 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.54 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.94/1.54 ) ), T ), Y ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.94/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.54 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.54 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.94/1.54 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.94/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.94/1.54 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.94/1.54 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.94/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.94/1.54 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.94/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.54 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha1( X, Y
% 0.94/1.54 , Z ), alpha14( X, Y, Z ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha14( X, Y, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ) }.
% 0.94/1.54 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.54 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ), alpha1( X, Y, Z ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ), alpha2( X, Y, Z ), alpha15( X, Y, Z ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ) }.
% 0.94/1.54 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ), Y ), alpha15( X, Y, Z ) }.
% 0.94/1.54 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.54 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), alpha2( X, Y, Z ) }.
% 0.94/1.54 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.54 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.54 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.54 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.54 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.94/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.94/1.54 .
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.94/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.94/1.54 .
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.54 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.54 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.94/1.54 ( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.54 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.94/1.54 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha3( X, Y, Z, T ),
% 0.94/1.54 alpha16( X, Y, Z, T ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.54 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.54 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha16( X, Y, Z, T ) }.
% 0.94/1.54 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.94/1.54 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.94/1.54 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha3( X, Y, Z, T ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha4( X, Y, Z, T ),
% 0.94/1.54 alpha17( X, Y, Z, T ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.54 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha17( X, Y, Z, T ) }.
% 0.94/1.54 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.54 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.54 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha4( X, Y, Z, T ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.54 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.94/1.54 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semidom( X ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.54 c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.94/1.54 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.54 .
% 0.94/1.54 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.94/1.54 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.94/1.54 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.94/1.54 ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.54 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.94/1.54 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.94/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.54 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.94/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.54 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.54 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.54 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.54 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.54 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.54 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.94/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.54 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.54 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.54 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.94/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.94/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.55 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.94/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.94/1.55 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.94/1.55 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.94/1.55 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.94/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.94/1.55 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.94/1.55 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.94/1.55 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.94/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.94/1.55 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.94/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.94/1.55 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.94/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.94/1.55 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.94/1.55 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.94/1.55 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.94/1.55 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.94/1.55 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.94/1.55 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.94/1.55 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), v_r ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), X ) ), skol4 ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol5( Z, T ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol5( X, Y ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol6( Z, T ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol6( X, Y ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7( Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol7( X ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol8( Z, T ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol8( X, Y ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol9( Z, T ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol9( X, Y ) ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.94/1.55 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.94/1.55 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.94/1.55 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha5
% 0.94/1.55 ( X, Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.94/1.55 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! alpha5( X, Y, Z ),
% 0.94/1.55 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.94/1.55 { ! alpha5( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.94/1.55 ( X ) ) }.
% 0.94/1.55 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.55 alpha5( X, Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.55 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.94/1.55 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.94/1.55 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10( Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol10( X ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol11( X ) ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.94/1.55 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.94/1.55 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.55 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.94/1.55 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.94/1.55 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.94/1.55 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.94/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.94/1.55 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.94/1.55 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.94/1.55 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol12( X, Y ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol13( X, Y ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.55 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.94/1.55 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.94/1.55 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.94/1.55 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.94/1.55 { alpha24( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.94/1.55 ( X, Y ), Z ) ) }.
% 0.94/1.55 { ! alpha24( X, Y, Z ), alpha25( X, Y, Z ), Z = Y }.
% 0.94/1.55 { ! alpha24( X, Y, Z ), alpha25( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! alpha25( X, Y, Z ), alpha24( X, Y, Z ) }.
% 0.94/1.55 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha24( X, Y, Z ) }.
% 0.94/1.55 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.94/1.55 }.
% 0.94/1.55 { ! alpha25( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.94/1.55 X, Y ), Z ) ), alpha25( X, Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.94/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol14( X, Y ) ) }.
% 0.94/1.55 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol15( X, Y ) ) }.
% 0.94/1.55 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.94/1.55 , X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.94/1.55 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.94/1.55 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.94/1.55 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.94/1.55 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.55 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.94/1.55 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.94/1.55 Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.55 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.94/1.55 , Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.94/1.55 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.94/1.55 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), X ) = X }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ) ) = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.94/1.55 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.94/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.94/1.55 .
% 0.94/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.94/1.55 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.94/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.94/1.55 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.94/1.55 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.94/1.55 ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.94/1.55 ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.94/1.55 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.94/1.55 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 Y ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.94/1.55 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.94/1.55 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.94/1.55 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.94/1.55 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.94/1.55 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.94/1.55 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.94/1.55 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.94/1.55 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.94/1.55 , Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.94/1.55 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.94/1.55 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.94/1.55 ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Nat_Onat ), X ), Y ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.94/1.55 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.94/1.55 , Y ), X ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ) }.
% 0.94/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.94/1.55 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.94/1.55 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.94/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.94/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.94/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.94/1.55 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.94/1.55 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.94/1.55 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.94/1.55 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol16( Z, Y
% 0.94/1.55 ), Y ) }.
% 0.94/1.55 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.94/1.55 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.55 skol16( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.94/1.55 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.94/1.55 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.94/1.55 , skol16( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.94/1.55 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 = Y }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Y ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.55 = Y }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.55 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.55 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.94/1.55 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Y ), Z ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.55 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Z ), Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.94/1.55 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.94/1.55 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.94/1.55 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.55 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.94/1.55 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.94/1.55 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.94/1.55 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.94/1.55 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.94/1.55 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.94/1.55 ) ), Y ) }.
% 0.94/1.55 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 Z, Y ) ) = Y }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.94/1.55 Y ) ) = Y }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.94/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.94/1.55 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.94/1.55 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Y ) = Y }.
% 0.94/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.94/1.55 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.94/1.55 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.94/1.55 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.94/1.55 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.94/1.55 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.94/1.55 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.94/1.55 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.94/1.55 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.94/1.55 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.94/1.55 ), c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.55 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.55 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.94/1.55 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.94/1.55 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.55 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Y ), Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.55 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , Y ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.55 , Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Z ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.55 Z ) = Y }.
% 0.94/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Y ) }.
% 0.94/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ) }.
% 0.94/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.94/1.55 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.94/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.55 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.55 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.55 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 0.94/1.55 }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.94/1.55 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.94/1.55 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ) }.
% 0.94/1.55 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_RealDef_Oreal, Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.94/1.55 , X ) ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.94/1.55 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.94/1.55 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.94/1.55 ( X ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , c_Groups_Oabs__class_Oabs( X, Y ) ), c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.94/1.55 X, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.94/1.55 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 0.94/1.55 }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) ) ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.94/1.55 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_RealDef_Oreal, Z, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.94/1.55 , X ) ) ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.94/1.55 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.94/1.55 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.94/1.55 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.94/1.55 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.94/1.55 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.94/1.55 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.94/1.55 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.94/1.55 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.55 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.55 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.55 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.94/1.55 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.94/1.55 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.94/1.55 Y = X }.
% 0.94/1.55 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.94/1.55 , X ) }.
% 0.94/1.55 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 0.94/1.55 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 0.94/1.55 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.94/1.55 ( tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.94/1.55 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.94/1.55 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.94/1.55 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.55 , c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.94/1.55 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_RComplete_Onatceiling( Y ), X ) }.
% 0.94/1.55 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.94/1.55 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.94/1.55 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.94/1.55 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.94/1.55 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.94/1.55 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Y ), Z = Y }.
% 0.94/1.55 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_RealDef_Oreal ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.55 , X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.94/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.55 , c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.94/1.55 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_RComplete_Onatceiling( X ), Y ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_RealDef_Oreal ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_RComplete_Onatfloor( X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.94/1.55 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.94/1.55 c_RComplete_Onatfloor( X ) = Y }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.94/1.55 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.94/1.55 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.94/1.55 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.94/1.55 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.94/1.55 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.94/1.55 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.94/1.55 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 0.94/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.55 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.94/1.55 , Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.94/1.55 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.94/1.55 , Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.94/1.55 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.55 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oabs__class_Oabs( X, Y ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.94/1.55 c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.55 ), c_Rings_Odvd__class_Odvd( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oabs__class_Oabs( X, Z )
% 0.94/1.55 = c_Groups_Oabs__class_Oabs( X, Y ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.94/1.55 }.
% 0.94/1.55 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.55 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.55 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.55 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.55 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.94/1.55 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.55 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.94/1.55 Z, T ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.55 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.55 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.55 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.55 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.94/1.55 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.94/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.94/1.55 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.94/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.94/1.55 X, T, Z ), Y ) }.
% 0.94/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.94/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha6( X
% 0.94/1.55 , Y, T ) }.
% 0.94/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha18( X
% 0.94/1.55 , Y, Z, T ) }.
% 0.94/1.55 { ! class_Fields_Ofield( X ), ! alpha6( X, Y, T ), ! alpha18( X, Y, Z, T )
% 0.94/1.55 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.94/1.55 ( X, T, Z ), Y ) }.
% 0.94/1.55 { ! alpha18( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.94/1.55 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha18( X, Y, Z, T ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha18( X
% 0.94/1.55 , Y, Z, T ) }.
% 0.94/1.55 { ! alpha6( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { Z = c_Groups_Ozero__class_Ozero( X ), alpha6( X, Y, Z ) }.
% 0.94/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha6( X
% 0.94/1.55 , Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.94/1.55 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.94/1.55 hAPP( Z, skol17( U, W, Z ) ) ) }.
% 0.94/1.55 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.94/1.55 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol17( X
% 0.94/1.55 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.94/1.55 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.94/1.55 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol32( X,
% 0.94/1.55 Y, Z ) ) ) ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.94/1.55 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.94/1.55 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.94/1.55 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.94/1.55 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, skol18( X, Y ) ) ), X ) ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.55 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.94/1.55 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.94/1.55 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.94/1.55 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ) ) = Y }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Z, Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.94/1.55 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.55 X ) ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.94/1.55 ( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.94/1.55 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.94/1.55 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.94/1.55 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha7( X, Y ), Y = X }
% 0.94/1.55 .
% 0.94/1.55 { ! alpha7( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! alpha7( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! alpha7( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), alpha7( X, Y ) }.
% 0.94/1.55 { ! alpha8( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! alpha8( X, Y ), ! Y = X }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha8( X, Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! alpha8( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! alpha8( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), alpha8( X, Y ) }.
% 0.94/1.55 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.94/1.55 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Nat_Onat, Y, Z ) }.
% 0.94/1.55 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Nat_Onat, Y, Z ) }.
% 0.94/1.55 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.94/1.55 , Z ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.94/1.55 Z, Y ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Nat_Onat, Y, Z ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.94/1.55 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.94/1.55 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.94/1.55 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.94/1.55 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.94/1.55 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.94/1.55 ), X ) ) }.
% 0.94/1.55 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.55 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.55 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.94/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.94/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.94/1.55 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.55 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.94/1.55 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) }.
% 0.94/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.55 = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.55 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.94/1.55 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Nat_Onat ) ) = Y }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.94/1.55 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.94/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.94/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.94/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.94/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.94/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.94/1.55 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.94/1.55 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.94/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.94/1.55 ), T ), U ), Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.55 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.94/1.55 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.94/1.55 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.94/1.55 ( hAPP( c_Power_Opower__class_Opower( X ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) =
% 0.94/1.55 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.94/1.55 ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.94/1.55 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.55 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.94/1.55 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.94/1.55 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.94/1.55 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.94/1.55 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.94/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.55 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), Y ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.94/1.55 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.94/1.55 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.94/1.55 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.94/1.55 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.94/1.55 Y ) ) ), Y ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.94/1.55 X ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.94/1.55 ( tc_Int_Oint, Y ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.94/1.55 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), c_Groups_Oabs__class_Oabs
% 0.94/1.55 ( tc_Int_Oint, Y ) = c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ),
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.94/1.55 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.55 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) = c_Groups_Oone__class_Oone
% 0.94/1.55 ( tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.94/1.55 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.94/1.55 , Z ), X ) ), T ) ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, U, T ) ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.94/1.55 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.94/1.55 ) ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Int_Oint, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.94/1.55 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.94/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.94/1.55 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.94/1.55 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.94/1.55 tc_Int_Oint, Y ) ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.94/1.55 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.94/1.55 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.94/1.55 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.94/1.55 { ! c_Nat_OSuc( X ) = X }.
% 0.94/1.55 { ! X = c_Nat_OSuc( X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.94/1.55 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.94/1.55 }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.94/1.55 c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.55 , c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.94/1.55 .
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.94/1.55 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.94/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.55 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.94/1.55 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.94/1.55 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.94/1.55 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.94/1.55 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.94/1.55 .
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.94/1.55 .
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.94/1.55 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.94/1.55 X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.94/1.55 }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.94/1.55 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.94/1.55 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.94/1.55 }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.94/1.55 = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ) ) }.
% 0.94/1.55 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.94/1.55 }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.94/1.55 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.94/1.55 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.94/1.55 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ) ) = X }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), X ) = X }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.55 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.94/1.55 ( tc_Int_Oint ) }.
% 0.94/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.94/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.94/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.94/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.94/1.55 tc_Int_Oint, X ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.94/1.55 tc_Int_Oint, X ) = X }.
% 0.94/1.55 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.94/1.55 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Int_Oint ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_Int_Oint ) ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.94/1.55 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.94/1.55 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.94/1.55 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 0.94/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.55 c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! alpha9( X, Y ), Y = c_Nat_OSuc( skol19( Z, Y ) ) }.
% 0.94/1.55 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol19( X,
% 0.94/1.55 Y ), X ) }.
% 0.94/1.55 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.94/1.55 ), alpha9( X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol20( X ) ) }.
% 0.94/1.55 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.94/1.55 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha10( X, Y ),
% 0.94/1.55 alpha19( X, Y ) }.
% 0.94/1.55 { ! alpha10( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.55 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! alpha19( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.55 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! alpha19( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! alpha19( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha19( X, Y ) }.
% 0.94/1.55 { ! alpha10( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! alpha10( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 0.94/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha11( X, Y ), alpha20( X
% 0.94/1.55 , Y ) }.
% 0.94/1.55 { ! alpha11( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! alpha20( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! alpha20( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! alpha20( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha20( X, Y ) }.
% 0.94/1.55 { ! alpha11( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! alpha11( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.94/1.55 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.94/1.55 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.94/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol21( X, Y ) ) ) }.
% 0.94/1.55 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.94/1.55 .
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.94/1.55 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.94/1.55 ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.94/1.55 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.94/1.55 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.94/1.55 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.94/1.55 ), X ) ) }.
% 0.94/1.55 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.94/1.55 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), Y ), Z = Y }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.94/1.55 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.55 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.94/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.94/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.94/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.94/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.94/1.55 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 0.94/1.55 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.55 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.94/1.55 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Int_Oint, Z, X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol22( X, Y, Z ) ) ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, c_Nat_OSuc( skol33( X, Y ) ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol36( X, Y, Z ) ) ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol38( T, U ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol36( X, Y, Z ) ) ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol38( X, Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol23( X, Y, Z ) ) ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.94/1.55 tc_Nat_Onat, c_Nat_OSuc( skol34( X, Y ) ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol37( X, Y, Z ) ) ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol39( T, U ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol37( X, Y, Z ) ) ),
% 0.94/1.55 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol39( X, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.94/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.55 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Nat_Onat ) ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.94/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.94/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.94/1.55 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.94/1.55 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.94/1.56 tc_Nat_Onat, Z, X ) }.
% 0.94/1.56 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Nat_Onat ), X ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.56 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.94/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.94/1.56 Y ) ) ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.94/1.56 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Y ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.94/1.56 ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.56 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.94/1.56 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.94/1.56 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.94/1.56 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.94/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.56 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.94/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.94/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.94/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.56 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.94/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.94/1.56 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.94/1.56 ( tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.56 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.56 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.56 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.94/1.56 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.94/1.56 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.94/1.56 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.56 tc_Nat_Onat, skol24( X, Y ), skol35( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 hAPP( Y, skol35( X, Y ) ), hAPP( Y, skol24( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.94/1.56 , Y ) }.
% 0.94/1.56 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.94/1.56 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.94/1.56 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol25( Z, Y ) ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.94/1.56 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, skol25( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.94/1.56 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.94/1.56 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, skol26( X ) ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, c_Nat_OSuc( skol26( X ) ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol27( Z, T ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol27( X, Y ) ), X ) =
% 0.94/1.56 Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.94/1.56 skol27( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol28( Z, T ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol28( X, Y ) ), X ) =
% 0.94/1.56 Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.56 ( X, Y ) ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.94/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.94/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.56 Z ) ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 W ) ), U ), Y ) }.
% 0.94/1.56 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.56 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ) }.
% 0.94/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.94/1.56 Z ) ), U ), T ) = Y }.
% 0.94/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.94/1.56 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.56 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.56 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.94/1.56 X, Y ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.56 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.56 X, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.94/1.56 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.94/1.56 X, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.94/1.56 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.94/1.56 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.94/1.56 , Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.94/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.94/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.94/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.56 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.94/1.56 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.94/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.94/1.56 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.94/1.56 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, Z, W ) ), U ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.56 X, W, Z ) ), U ), T ), Y ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), U ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.94/1.56 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.94/1.56 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.94/1.56 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.94/1.56 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.94/1.56 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.94/1.56 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.94/1.56 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.94/1.56 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.94/1.56 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.94/1.56 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, Y, Z ) ) }.
% 0.94/1.56 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.94/1.56 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.94/1.56 hAPP( Z, Y ) ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.94/1.56 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.94/1.56 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.94/1.56 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.94/1.56 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.94/1.56 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.94/1.56 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.94/1.56 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.94/1.56 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, Z, Y ), T ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.94/1.56 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( X, Z, Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.94/1.56 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.94/1.56 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.94/1.56 Y ) ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.94/1.56 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.94/1.56 ( tc_Int_Oint ) ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.56 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.56 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( X, T, Y ) ) ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.94/1.56 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.94/1.56 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, T, skol29( X, U, W, T ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.94/1.56 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.94/1.56 hAPP( Z, T ), hAPP( Z, skol29( X, Y, Z, T ) ) ) ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.94/1.56 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Int_Oint, X, Y ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.94/1.56 ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.94/1.56 , ! alpha12( X, Y, Z ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.94/1.56 , ! alpha21( X, Y, Z ) }.
% 0.94/1.56 { alpha12( X, Y, Z ), alpha21( X, Y, Z ), hBOOL( hAPP( Z,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.56 { ! alpha21( X, Y, Z ), ! hBOOL( hAPP( Z, skol30( T, U, Z ) ) ) }.
% 0.94/1.56 { ! alpha21( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.94/1.56 skol30( X, Y, Z ) ) }.
% 0.94/1.56 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.94/1.56 ) ), alpha21( X, Y, Z ) }.
% 0.94/1.56 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.94/1.56 }.
% 0.94/1.56 { ! alpha12( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12( X, Y, Z ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.94/1.56 , alpha13( X, Y, Z ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.94/1.56 , alpha22( X, Y, Z ) }.
% 0.94/1.56 { ! alpha13( X, Y, Z ), ! alpha22( X, Y, Z ), hBOOL( hAPP( Z,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.56 { ! alpha22( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.94/1.56 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, skol31( T, U, Z ) ) ), alpha22( X, Y, Z ) }.
% 0.94/1.56 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol31( X, Y, Z ) ),
% 0.94/1.56 alpha22( X, Y, Z ) }.
% 0.94/1.56 { ! alpha13( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.94/1.56 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha13( X, Y, Z ) }
% 0.94/1.56 .
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13
% 0.94/1.56 ( X, Y, Z ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.56 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.94/1.56 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.94/1.56 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 0.94/1.56 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.94/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 0.94/1.56 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.94/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.94/1.56 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), X ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.94/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.56 c_RComplete_Onatfloor( X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.56 c_RComplete_Onatceiling( X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 0.94/1.56 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.94/1.56 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.94/1.56 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.56 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.94/1.56 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.94/1.56 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.94/1.56 ( tc_fun( Y, X ) ) }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.94/1.56 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.94/1.56 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.94/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.56 tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.94/1.56 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.94/1.56 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.94/1.56 { class_Power_Opower( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.94/1.56 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.94/1.56 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.94/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.56 tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.94/1.56 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.94/1.56 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.94/1.56 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.94/1.56 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.94/1.56 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.94/1.56 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.94/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.56 tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.94/1.56 .
% 0.94/1.56 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oabs__if( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 0.94/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.56 tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ),
% 0.94/1.56 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.94/1.56 X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.94/1.56 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.56 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.94/1.56 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.94/1.56 ( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.94/1.56 ( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), class_Groups_Oabs__if(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.94/1.56 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_c____ ), hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), v_r ), v_m____ )
% 0.94/1.56 ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.94/1.56 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm(
% 0.94/1.56 tc_Complex_Ocomplex, v_c____ ) ), c_Groups_Oabs__class_Oabs(
% 0.94/1.56 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_RealDef_Oreal ), v_r ), v_m____ ) ) ) ) }.
% 0.94/1.56
% 0.94/1.56 *** allocated 15000 integers for clauses
% 0.94/1.56 *** allocated 22500 integers for clauses
% 0.94/1.56 *** allocated 33750 integers for clauses
% 0.94/1.56 *** allocated 50625 integers for clauses
% 0.94/1.56 *** allocated 75937 integers for clauses
% 0.94/1.56 percentage equality = 0.247042, percentage horn = 0.921105
% 0.94/1.56 This is a problem with some equality
% 0.94/1.56
% 0.94/1.56
% 0.94/1.56
% 0.94/1.56 Options Used:
% 0.94/1.56
% 0.94/1.56 useres = 1
% 0.94/1.56 useparamod = 1
% 0.94/1.56 useeqrefl = 1
% 0.94/1.56 useeqfact = 1
% 0.94/1.56 usefactor = 1
% 0.94/1.56 usesimpsplitting = 0
% 0.94/1.56 usesimpdemod = 5
% 0.94/1.56 usesimpres = 3
% 0.94/1.56
% 0.94/1.56 resimpinuse = 1000
% 0.94/1.56 resimpclauses = 20000
% 0.94/1.56 substype = eqrewr
% 0.94/1.56 backwardsubs = 1
% 0.94/1.56 selectoldest = 5
% 0.94/1.56
% 0.94/1.56 litorderings [0] = split
% 0.94/1.56 litorderings [1] = extend the termordering, first sorting on arguments
% 0.94/1.56
% 0.94/1.56 termordering = kbo
% 0.94/1.56
% 0.94/1.56 litapriori = 0
% 0.94/1.56 termapriori = 1
% 0.94/1.56 litaposteriori = 0
% 0.94/1.56 termaposteriori = 0
% 0.94/1.56 demodaposteriori = 0
% 0.94/1.56 ordereqreflfact = 0
% 0.94/1.56
% 0.94/1.56 litselect = negord
% 0.94/1.56
% 0.94/1.56 maxweight = 15
% 0.94/1.56 maxdepth = 30000
% 0.94/1.56 maxlength = 115
% 0.94/1.56 maxnrvars = 195
% 0.94/1.56 excuselevel = 1
% 0.94/1.56 increasemaxweight = 1
% 0.94/1.56
% 0.94/1.56 maxselected = 10000000
% 0.94/1.56 maxnrclauses = 10000000
% 0.94/1.56
% 0.94/1.56 showgenerated = 0
% 0.94/1.56 showkept = 0
% 0.94/1.56 showselected = 0
% 0.94/1.56 showdeleted = 0
% 0.94/1.56 showresimp = 1
% 0.94/1.56 showstatus = 2000
% 0.94/1.56
% 0.94/1.56 prologoutput = 0
% 0.94/1.56 nrgoals = 5000000
% 0.94/1.56 totalproof = 1
% 0.94/1.56
% 0.94/1.56 Symbols occurring in the translation:
% 0.94/1.56
% 0.94/1.56 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.94/1.56 . [1, 2] (w:1, o:195, a:1, s:1, b:0),
% 0.94/1.56 ! [4, 1] (w:0, o:107, a:1, s:1, b:0),
% 0.94/1.56 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.56 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.56 hAPP [38, 2] (w:1, o:219, a:1, s:1, b:0),
% 0.94/1.56 tc_RealDef_Oreal [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.94/1.56 tc_Complex_Ocomplex [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.94/1.56 v_z____ [41, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm [42, 2] (w:1, o:220, a:1, s:1, b:0),
% 0.94/1.56
% 0.94/1.56 v_r [43, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq [44, 3] (w:1, o:261, a:1, s:1, b:0)
% 0.94/1.56 ,
% 0.94/1.56 class_RealVector_Oreal__normed__vector [48, 1] (w:1, o:112, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 c_Groups_Oplus__class_Oplus [49, 3] (w:1, o:262, a:1, s:1, b:0),
% 0.94/1.56 class_RealVector_Oreal__normed__algebra [50, 1] (w:1, o:113, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 c_Groups_Otimes__class_Otimes [51, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.94/1.56 v_cs____ [53, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.94/1.56 c_Polynomial_Opoly [54, 2] (w:1, o:221, a:1, s:1, b:0),
% 0.94/1.56 v_m____ [55, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.94/1.56 class_RealVector_Oreal__normed__algebra__1 [56, 1] (w:1, o:115, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 c_Groups_Oone__class_Oone [57, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.94/1.56 c_Groups_Ozero__class_Ozero [58, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.94/1.56 class_RealVector_Oreal__normed__div__algebra [59, 1] (w:1, o:118, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 class_Groups_Oordered__ab__group__add__abs [62, 1] (w:1, o:120, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 c_Groups_Oabs__class_Oabs [63, 2] (w:1, o:222, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Ocomm__semiring__1 [65, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.94/1.56 v_c____ [66, 0] (w:1, o:42, a:1, s:1, b:0),
% 0.94/1.56 c_Orderings_Oord__class_Oless [67, 3] (w:1, o:263, a:1, s:1, b:0),
% 0.94/1.56 class_Orderings_Opreorder [68, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.94/1.56 class_Orderings_Olinorder [72, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Ozero [73, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Olinordered__ab__group__add [75, 1] (w:1, o:130, a:1, s:
% 0.94/1.56 1, b:0),
% 0.94/1.56 class_Groups_Oordered__comm__monoid__add [76, 1] (w:1, o:131, a:1, s:
% 0.94/1.56 1, b:0),
% 0.94/1.56 class_Orderings_Oorder [77, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.94/1.56 class_Orderings_Oord [79, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Oordered__ab__semigroup__add__imp__le [81, 1] (w:1, o:
% 0.94/1.56 132, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Oordered__cancel__ab__semigroup__add [83, 1] (w:1, o:133
% 0.94/1.56 , a:1, s:1, b:0),
% 0.94/1.56 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [86
% 0.94/1.56 , 1] (w:1, o:160, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Ocomm__monoid__add [87, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.94/1.56
% 0.94/1.56 class_Groups_Omonoid__add [88, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.94/1.56 tc_fun [92, 2] (w:1, o:245, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Oab__semigroup__mult [97, 1] (w:1, o:163, a:1, s:1, b:0)
% 0.94/1.56 ,
% 0.94/1.56 class_Groups_Ocancel__semigroup__add [99, 1] (w:1, o:164, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Groups_Ocancel__ab__semigroup__add [100, 1] (w:1, o:165, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 class_Groups_Oab__semigroup__add [101, 1] (w:1, o:166, a:1, s:1, b:0)
% 0.94/1.56 ,
% 0.94/1.56 class_Groups_Oone [102, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.94/1.56 class_Groups_Oordered__ab__semigroup__add [103, 1] (w:1, o:168, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 class_Groups_Ocomm__monoid__mult [111, 1] (w:1, o:169, a:1, s:1, b:0)
% 0.94/1.56 ,
% 0.94/1.56 class_Groups_Omonoid__mult [112, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.94/1.56 c_Polynomial_OpCons [113, 3] (w:1, o:265, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Olinordered__semiring__1__strict [116, 1] (w:1, o:136, a:
% 0.94/1.56 1, s:1, b:0),
% 0.94/1.56 class_Rings_Olinordered__semiring__1 [117, 1] (w:1, o:137, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Rings_Oordered__ring__abs [118, 1] (w:1, o:139, a:1, s:1, b:0)
% 0.94/1.56 ,
% 0.94/1.56 class_Rings_Olinordered__idom [119, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Omult__zero [126, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Oring__no__zero__divisors [127, 1] (w:1, o:146, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Rings_Ono__zero__divisors [128, 1] (w:1, o:138, a:1, s:1, b:0)
% 0.94/1.56 ,
% 0.94/1.56 class_Rings_Ozero__neq__one [129, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Ocomm__semiring [130, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Osemiring [132, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Olinordered__ring [133, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Olinordered__ring__strict [134, 1] (w:1, o:135, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Rings_Oordered__cancel__semiring [135, 1] (w:1, o:153, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Rings_Oordered__ring [136, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Oordered__semiring [137, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.94/1.56
% 0.94/1.56 class_Rings_Oordered__comm__semiring [138, 1] (w:1, o:156, a:1, s:1
% 0.94/1.56 , b:0),
% 0.94/1.56 class_Rings_Olinordered__comm__semiring__strict [139, 1] (w:1, o:141
% 0.94/1.56 , a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Olinordered__semiring__strict [140, 1] (w:1, o:142, a:1
% 0.94/1.56 , s:1, b:0),
% 0.94/1.56 class_Rings_Olinordered__semidom [141, 1] (w:1, o:143, a:1, s:1, b:0)
% 0.94/1.56 ,
% 0.94/1.56 class_Rings_Olinordered__semiring [143, 1] (w:1, o:144, a:1, s:1, b:0
% 0.94/1.56 ),
% 0.94/1.56 class_Rings_Ocomm__semiring__0 [145, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.94/1.56
% 0.94/1.56 class_Int_Oring__char__0 [148, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.94/1.56 class_Rings_Oidom [149, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.94/1.56 tc_Polynomial_Opoly [150, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.94/1.56 c_Polynomial_Opcompose [155, 3] (w:1, o:266, a:1, s:1, b:0),
% 0.94/1.56 c_Polynomial_Opos__poly [156, 2] (w:1, o:246, a:1, s:1, b:0),
% 2.12/2.48 c_Polynomial_Oorder [157, 3] (w:1, o:264, a:1, s:1, b:0),
% 2.12/2.48 tc_Nat_Onat [158, 0] (w:1, o:82, a:1, s:1, b:0),
% 2.12/2.48 c_Polynomial_Opoly__rec [159, 5] (w:1, o:300, a:1, s:1, b:0),
% 2.12/2.48 c_fequal [160, 2] (w:1, o:247, a:1, s:1, b:0),
% 2.12/2.48 c_If [161, 4] (w:1, o:293, a:1, s:1, b:0),
% 2.12/2.48 c_Groups_Osgn__class_Osgn [162, 2] (w:1, o:248, a:1, s:1, b:0),
% 2.12/2.48 c_Polynomial_Osmult [163, 3] (w:1, o:267, a:1, s:1, b:0),
% 2.12/2.48 hBOOL [168, 1] (w:1, o:178, a:1, s:1, b:0),
% 2.12/2.48 class_Groups_Osgn__if [174, 1] (w:1, o:179, a:1, s:1, b:0),
% 2.12/2.48 c_Polynomial_Osynthetic__div [175, 3] (w:1, o:268, a:1, s:1, b:0),
% 2.12/2.48 class_Rings_Ocomm__ring__1 [176, 1] (w:1, o:121, a:1, s:1, b:0),
% 2.12/2.48 c_Groups_Ouminus__class_Ouminus [177, 2] (w:1, o:249, a:1, s:1, b:0)
% 2.12/2.48 ,
% 2.12/2.48 c_RComplete_Onatceiling [179, 1] (w:1, o:180, a:1, s:1, b:0),
% 2.12/2.48 c_RComplete_Onatfloor [180, 1] (w:1, o:181, a:1, s:1, b:0),
% 2.12/2.48 class_Groups_Ogroup__add [181, 1] (w:1, o:182, a:1, s:1, b:0),
% 2.12/2.48 class_Groups_Oordered__ab__group__add [182, 1] (w:1, o:183, a:1, s:1
% 2.12/2.48 , b:0),
% 2.12/2.48 class_Rings_Oring [183, 1] (w:1, o:149, a:1, s:1, b:0),
% 2.12/2.48 class_Groups_Oab__group__add [184, 1] (w:1, o:184, a:1, s:1, b:0),
% 2.12/2.48 class_Rings_Ocomm__ring [185, 1] (w:1, o:122, a:1, s:1, b:0),
% 2.12/2.48 class_Rings_Oring__1__no__zero__divisors [186, 1] (w:1, o:150, a:1
% 2.12/2.48 , s:1, b:0),
% 2.12/2.48 class_Groups_Oabs__if [188, 1] (w:1, o:185, a:1, s:1, b:0),
% 2.12/2.48 c_RealDef_Oreal [189, 2] (w:1, o:250, a:1, s:1, b:0),
% 2.12/2.48 class_Lattices_Oboolean__algebra [190, 1] (w:1, o:187, a:1, s:1, b:0)
% 2.12/2.48 ,
% 2.12/2.48 class_Lattices_Oab__semigroup__idem__mult [191, 1] (w:1, o:186, a:1
% 2.12/2.48 , s:1, b:0),
% 2.12/2.48 class_Groups_Ouminus [193, 1] (w:1, o:188, a:1, s:1, b:0),
% 2.12/2.48 c_Rings_Odvd__class_Odvd [194, 3] (w:1, o:269, a:1, s:1, b:0),
% 2.12/2.48 c_Complex_Oexpi [195, 1] (w:1, o:189, a:1, s:1, b:0),
% 2.12/2.48 class_Rings_Odvd [196, 1] (w:1, o:158, a:1, s:1, b:0),
% 2.12/2.48 class_Fields_Ofield [197, 1] (w:1, o:119, a:1, s:1, b:0),
% 2.12/2.48 class_Rings_Osemiring__0 [198, 1] (w:1, o:159, a:1, s:1, b:0),
% 2.12/2.48 c_Power_Opower__class_Opower [199, 1] (w:1, o:190, a:1, s:1, b:0),
% 2.12/2.48 tc_Int_Oint [201, 0] (w:1, o:91, a:1, s:1, b:0),
% 2.12/2.48 class_Power_Opower [202, 1] (w:1, o:191, a:1, s:1, b:0),
% 2.12/2.48 class_Rings_Oring__1 [203, 1] (w:1, o:151, a:1, s:1, b:0),
% 2.12/2.48 c_Nat_OSuc [205, 1] (w:1, o:192, a:1, s:1, b:0),
% 2.12/2.48 c_Power_Opower_Opower [218, 3] (w:1, o:270, a:1, s:1, b:0),
% 2.12/2.48 c_SEQ_Odecseq [219, 2] (w:1, o:251, a:1, s:1, b:0),
% 2.12/2.48 c_Groups_Ominus__class_Ominus [223, 3] (w:1, o:271, a:1, s:1, b:0),
% 2.12/2.48 class_Groups_Ominus [227, 1] (w:1, o:193, a:1, s:1, b:0),
% 2.12/2.48 c_Nat__Transfer_Otsub [229, 2] (w:1, o:252, a:1, s:1, b:0),
% 2.12/2.48 class_Groups_Ocancel__comm__monoid__add [234, 1] (w:1, o:194, a:1, s:
% 2.12/2.48 1, b:0),
% 2.12/2.48 tc_HOL_Obool [236, 0] (w:1, o:90, a:1, s:1, b:0),
% 2.12/2.48 alpha1 [237, 3] (w:1, o:272, a:1, s:1, b:1),
% 2.12/2.48 alpha2 [238, 3] (w:1, o:277, a:1, s:1, b:1),
% 2.12/2.48 alpha3 [239, 4] (w:1, o:294, a:1, s:1, b:1),
% 2.12/2.48 alpha4 [240, 4] (w:1, o:295, a:1, s:1, b:1),
% 2.12/2.48 alpha5 [241, 3] (w:1, o:278, a:1, s:1, b:1),
% 2.12/2.48 alpha6 [242, 3] (w:1, o:279, a:1, s:1, b:1),
% 2.12/2.48 alpha7 [243, 2] (w:1, o:253, a:1, s:1, b:1),
% 2.12/2.48 alpha8 [244, 2] (w:1, o:254, a:1, s:1, b:1),
% 2.12/2.48 alpha9 [245, 2] (w:1, o:255, a:1, s:1, b:1),
% 2.12/2.48 alpha10 [246, 2] (w:1, o:256, a:1, s:1, b:1),
% 2.12/2.48 alpha11 [247, 2] (w:1, o:257, a:1, s:1, b:1),
% 2.12/2.48 alpha12 [248, 3] (w:1, o:273, a:1, s:1, b:1),
% 2.12/2.48 alpha13 [249, 3] (w:1, o:274, a:1, s:1, b:1),
% 2.12/2.48 alpha14 [250, 3] (w:1, o:275, a:1, s:1, b:1),
% 2.12/2.48 alpha15 [251, 3] (w:1, o:276, a:1, s:1, b:1),
% 2.12/2.48 alpha16 [252, 4] (w:1, o:296, a:1, s:1, b:1),
% 2.12/2.48 alpha17 [253, 4] (w:1, o:297, a:1, s:1, b:1),
% 2.12/2.48 alpha18 [254, 4] (w:1, o:298, a:1, s:1, b:1),
% 2.12/2.48 alpha19 [255, 2] (w:1, o:258, a:1, s:1, b:1),
% 2.12/2.48 alpha20 [256, 2] (w:1, o:259, a:1, s:1, b:1),
% 2.12/2.48 alpha21 [257, 3] (w:1, o:280, a:1, s:1, b:1),
% 2.12/2.48 alpha22 [258, 3] (w:1, o:281, a:1, s:1, b:1),
% 2.12/2.48 alpha23 [259, 2] (w:1, o:260, a:1, s:1, b:1),
% 2.12/2.48 alpha24 [260, 3] (w:1, o:282, a:1, s:1, b:1),
% 16.79/17.14 alpha25 [261, 3] (w:1, o:283, a:1, s:1, b:1),
% 16.79/17.14 skol1 [262, 2] (w:1, o:223, a:1, s:1, b:1),
% 16.79/17.14 skol2 [263, 0] (w:1, o:11, a:1, s:1, b:1),
% 16.79/17.14 skol3 [264, 3] (w:1, o:286, a:1, s:1, b:1),
% 16.79/17.14 skol4 [265, 0] (w:1, o:12, a:1, s:1, b:1),
% 16.79/17.14 skol5 [266, 2] (w:1, o:224, a:1, s:1, b:1),
% 16.79/17.14 skol6 [267, 2] (w:1, o:225, a:1, s:1, b:1),
% 16.79/17.14 skol7 [268, 1] (w:1, o:172, a:1, s:1, b:1),
% 16.79/17.14 skol8 [269, 2] (w:1, o:226, a:1, s:1, b:1),
% 16.79/17.14 skol9 [270, 2] (w:1, o:227, a:1, s:1, b:1),
% 16.79/17.14 skol10 [271, 1] (w:1, o:173, a:1, s:1, b:1),
% 16.79/17.14 skol11 [272, 1] (w:1, o:174, a:1, s:1, b:1),
% 16.79/17.14 skol12 [273, 2] (w:1, o:228, a:1, s:1, b:1),
% 16.79/17.14 skol13 [274, 2] (w:1, o:229, a:1, s:1, b:1),
% 16.79/17.14 skol14 [275, 2] (w:1, o:230, a:1, s:1, b:1),
% 16.79/17.14 skol15 [276, 2] (w:1, o:231, a:1, s:1, b:1),
% 16.79/17.14 skol16 [277, 2] (w:1, o:232, a:1, s:1, b:1),
% 16.79/17.14 skol17 [278, 3] (w:1, o:287, a:1, s:1, b:1),
% 16.79/17.14 skol18 [279, 2] (w:1, o:233, a:1, s:1, b:1),
% 16.79/17.14 skol19 [280, 2] (w:1, o:234, a:1, s:1, b:1),
% 16.79/17.14 skol20 [281, 1] (w:1, o:175, a:1, s:1, b:1),
% 16.79/17.14 skol21 [282, 2] (w:1, o:235, a:1, s:1, b:1),
% 16.79/17.14 skol22 [283, 3] (w:1, o:284, a:1, s:1, b:1),
% 16.79/17.14 skol23 [284, 3] (w:1, o:285, a:1, s:1, b:1),
% 16.79/17.14 skol24 [285, 2] (w:1, o:236, a:1, s:1, b:1),
% 16.79/17.14 skol25 [286, 2] (w:1, o:237, a:1, s:1, b:1),
% 16.79/17.14 skol26 [287, 1] (w:1, o:176, a:1, s:1, b:1),
% 16.79/17.14 skol27 [288, 2] (w:1, o:238, a:1, s:1, b:1),
% 16.79/17.14 skol28 [289, 2] (w:1, o:239, a:1, s:1, b:1),
% 16.79/17.14 skol29 [290, 4] (w:1, o:299, a:1, s:1, b:1),
% 16.79/17.14 skol30 [291, 3] (w:1, o:288, a:1, s:1, b:1),
% 16.79/17.14 skol31 [292, 3] (w:1, o:289, a:1, s:1, b:1),
% 16.79/17.14 skol32 [293, 3] (w:1, o:290, a:1, s:1, b:1),
% 16.79/17.14 skol33 [294, 2] (w:1, o:240, a:1, s:1, b:1),
% 16.79/17.14 skol34 [295, 2] (w:1, o:241, a:1, s:1, b:1),
% 16.79/17.14 skol35 [296, 2] (w:1, o:242, a:1, s:1, b:1),
% 16.79/17.14 skol36 [297, 3] (w:1, o:291, a:1, s:1, b:1),
% 16.79/17.14 skol37 [298, 3] (w:1, o:292, a:1, s:1, b:1),
% 16.79/17.14 skol38 [299, 2] (w:1, o:243, a:1, s:1, b:1),
% 16.79/17.14 skol39 [300, 2] (w:1, o:244, a:1, s:1, b:1).
% 16.79/17.14
% 16.79/17.14
% 16.79/17.14 Starting Search:
% 16.79/17.14
% 16.79/17.14 *** allocated 113905 integers for clauses
% 16.79/17.14 *** allocated 170857 integers for clauses
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14
% 16.79/17.14 Intermediate Status:
% 16.79/17.14 Generated: 2973
% 16.79/17.14 Kept: 2021
% 16.79/17.14 Inuse: 61
% 16.79/17.14 Deleted: 0
% 16.79/17.14 Deletedinuse: 0
% 16.79/17.14
% 16.79/17.14 *** allocated 256285 integers for clauses
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14 *** allocated 170857 integers for termspace/termends
% 16.79/17.14 *** allocated 384427 integers for clauses
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14
% 16.79/17.14 Intermediate Status:
% 16.79/17.14 Generated: 6647
% 16.79/17.14 Kept: 4043
% 16.79/17.14 Inuse: 193
% 16.79/17.14 Deleted: 3
% 16.79/17.14 Deletedinuse: 0
% 16.79/17.14
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14 *** allocated 256285 integers for termspace/termends
% 16.79/17.14
% 16.79/17.14 Intermediate Status:
% 16.79/17.14 Generated: 10128
% 16.79/17.14 Kept: 6304
% 16.79/17.14 Inuse: 268
% 16.79/17.14 Deleted: 3
% 16.79/17.14 Deletedinuse: 0
% 16.79/17.14
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14 *** allocated 576640 integers for clauses
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14
% 16.79/17.14 Intermediate Status:
% 16.79/17.14 Generated: 13822
% 16.79/17.14 Kept: 8312
% 16.79/17.14 Inuse: 348
% 16.79/17.14 Deleted: 3
% 16.79/17.14 Deletedinuse: 0
% 16.79/17.14
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14 *** allocated 384427 integers for termspace/termends
% 16.79/17.14
% 16.79/17.14 Intermediate Status:
% 16.79/17.14 Generated: 16994
% 16.79/17.14 Kept: 10502
% 16.79/17.14 Inuse: 393
% 16.79/17.14 Deleted: 3
% 16.79/17.14 Deletedinuse: 0
% 16.79/17.14
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14 *** allocated 864960 integers for clauses
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14
% 16.79/17.14 Intermediate Status:
% 16.79/17.14 Generated: 20102
% 16.79/17.14 Kept: 12524
% 16.79/17.14 Inuse: 441
% 16.79/17.14 Deleted: 3
% 16.79/17.14 Deletedinuse: 0
% 16.79/17.14
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14
% 16.79/17.14 Intermediate Status:
% 16.79/17.14 Generated: 23193
% 16.79/17.14 Kept: 14648
% 16.79/17.14 Inuse: 472
% 16.79/17.14 Deleted: 4
% 16.79/17.14 Deletedinuse: 0
% 16.79/17.14
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14 *** allocated 576640 integers for termspace/termends
% 16.79/17.14
% 16.79/17.14 Intermediate Status:
% 16.79/17.14 Generated: 28516
% 16.79/17.14 Kept: 16715
% 16.79/17.14 Inuse: 497
% 16.79/17.14 Deleted: 4
% 16.79/17.14 Deletedinuse: 0
% 16.79/17.14
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14 *** allocated 1297440 integers for clauses
% 16.79/17.14
% 16.79/17.14 Intermediate Status:
% 16.79/17.14 Generated: 39919
% 16.79/17.14 Kept: 19155
% 16.79/17.14 Inuse: 527
% 16.79/17.14 Deleted: 4
% 16.79/17.14 Deletedinuse: 0
% 16.79/17.14
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14 Resimplifying inuse:
% 16.79/17.14 Done
% 16.79/17.14
% 16.79/17.14 Resimplifying clauses:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 43339
% 64.58/64.94 Kept: 21179
% 64.58/64.94 Inuse: 550
% 64.58/64.94 Deleted: 295
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 50046
% 64.58/64.94 Kept: 23614
% 64.58/64.94 Inuse: 577
% 64.58/64.94 Deleted: 295
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 *** allocated 864960 integers for termspace/termends
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 54700
% 64.58/64.94 Kept: 25707
% 64.58/64.94 Inuse: 622
% 64.58/64.94 Deleted: 295
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 61527
% 64.58/64.94 Kept: 27991
% 64.58/64.94 Inuse: 647
% 64.58/64.94 Deleted: 295
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 *** allocated 1946160 integers for clauses
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 70434
% 64.58/64.94 Kept: 30751
% 64.58/64.94 Inuse: 657
% 64.58/64.94 Deleted: 295
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 77432
% 64.58/64.94 Kept: 33926
% 64.58/64.94 Inuse: 697
% 64.58/64.94 Deleted: 295
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 81735
% 64.58/64.94 Kept: 36026
% 64.58/64.94 Inuse: 732
% 64.58/64.94 Deleted: 295
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 *** allocated 1297440 integers for termspace/termends
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 97502
% 64.58/64.94 Kept: 38514
% 64.58/64.94 Inuse: 742
% 64.58/64.94 Deleted: 295
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 104636
% 64.58/64.94 Kept: 40663
% 64.58/64.94 Inuse: 767
% 64.58/64.94 Deleted: 295
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying clauses:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 *** allocated 2919240 integers for clauses
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 110152
% 64.58/64.94 Kept: 42741
% 64.58/64.94 Inuse: 802
% 64.58/64.94 Deleted: 425
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 116353
% 64.58/64.94 Kept: 45127
% 64.58/64.94 Inuse: 832
% 64.58/64.94 Deleted: 425
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 124119
% 64.58/64.94 Kept: 47194
% 64.58/64.94 Inuse: 847
% 64.58/64.94 Deleted: 425
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 136378
% 64.58/64.94 Kept: 49225
% 64.58/64.94 Inuse: 875
% 64.58/64.94 Deleted: 425
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 *** allocated 1946160 integers for termspace/termends
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 142731
% 64.58/64.94 Kept: 51240
% 64.58/64.94 Inuse: 907
% 64.58/64.94 Deleted: 425
% 64.58/64.94 Deletedinuse: 0
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 153104
% 64.58/64.94 Kept: 54043
% 64.58/64.94 Inuse: 932
% 64.58/64.94 Deleted: 429
% 64.58/64.94 Deletedinuse: 4
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 163271
% 64.58/64.94 Kept: 56745
% 64.58/64.94 Inuse: 947
% 64.58/64.94 Deleted: 429
% 64.58/64.94 Deletedinuse: 4
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 180118
% 64.58/64.94 Kept: 60236
% 64.58/64.94 Inuse: 972
% 64.58/64.94 Deleted: 429
% 64.58/64.94 Deletedinuse: 4
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying clauses:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 195450
% 64.58/64.94 Kept: 63079
% 64.58/64.94 Inuse: 987
% 64.58/64.94 Deleted: 625
% 64.58/64.94 Deletedinuse: 4
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 *** allocated 4378860 integers for clauses
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 203457
% 64.58/64.94 Kept: 65082
% 64.58/64.94 Inuse: 1021
% 64.58/64.94 Deleted: 627
% 64.58/64.94 Deletedinuse: 6
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 211029
% 64.58/64.94 Kept: 69719
% 64.58/64.94 Inuse: 1027
% 64.58/64.94 Deleted: 627
% 64.58/64.94 Deletedinuse: 6
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 231738
% 64.58/64.94 Kept: 72321
% 64.58/64.94 Inuse: 1042
% 64.58/64.94 Deleted: 627
% 64.58/64.94 Deletedinuse: 6
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 *** allocated 2919240 integers for termspace/termends
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 259820
% 64.58/64.94 Kept: 75781
% 64.58/64.94 Inuse: 1052
% 64.58/64.94 Deleted: 627
% 64.58/64.94 Deletedinuse: 6
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94 Resimplifying inuse:
% 64.58/64.94 Done
% 64.58/64.94
% 64.58/64.94
% 64.58/64.94 Intermediate Status:
% 64.58/64.94 Generated: 276425
% 64.58/64.94 Kept: 79153
% 64.58/64.94 Inuse: 1058
% 64.58/64.94 Deleted: 627
% 64.58/64.94 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying clauses:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 283748
% 175.26/175.65 Kept: 81373
% 175.26/175.65 Inuse: 1092
% 175.26/175.65 Deleted: 4356
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 289813
% 175.26/175.65 Kept: 83380
% 175.26/175.65 Inuse: 1136
% 175.26/175.65 Deleted: 4356
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 296136
% 175.26/175.65 Kept: 85403
% 175.26/175.65 Inuse: 1174
% 175.26/175.65 Deleted: 4356
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 304470
% 175.26/175.65 Kept: 87699
% 175.26/175.65 Inuse: 1197
% 175.26/175.65 Deleted: 4356
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 315165
% 175.26/175.65 Kept: 89906
% 175.26/175.65 Inuse: 1217
% 175.26/175.65 Deleted: 4356
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 325341
% 175.26/175.65 Kept: 91960
% 175.26/175.65 Inuse: 1237
% 175.26/175.65 Deleted: 4356
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 333023
% 175.26/175.65 Kept: 94123
% 175.26/175.65 Inuse: 1262
% 175.26/175.65 Deleted: 4356
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 339699
% 175.26/175.65 Kept: 96172
% 175.26/175.65 Inuse: 1287
% 175.26/175.65 Deleted: 4356
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 345842
% 175.26/175.65 Kept: 98261
% 175.26/175.65 Inuse: 1317
% 175.26/175.65 Deleted: 4356
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 *** allocated 6568290 integers for clauses
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 350730
% 175.26/175.65 Kept: 100275
% 175.26/175.65 Inuse: 1359
% 175.26/175.65 Deleted: 4356
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying clauses:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 355608
% 175.26/175.65 Kept: 102402
% 175.26/175.65 Inuse: 1417
% 175.26/175.65 Deleted: 4512
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 366805
% 175.26/175.65 Kept: 104671
% 175.26/175.65 Inuse: 1452
% 175.26/175.65 Deleted: 4512
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 *** allocated 4378860 integers for termspace/termends
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 380604
% 175.26/175.65 Kept: 107833
% 175.26/175.65 Inuse: 1462
% 175.26/175.65 Deleted: 4512
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 387864
% 175.26/175.65 Kept: 110096
% 175.26/175.65 Inuse: 1482
% 175.26/175.65 Deleted: 4512
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 398228
% 175.26/175.65 Kept: 112509
% 175.26/175.65 Inuse: 1497
% 175.26/175.65 Deleted: 4512
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 405168
% 175.26/175.65 Kept: 114674
% 175.26/175.65 Inuse: 1512
% 175.26/175.65 Deleted: 4512
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 410486
% 175.26/175.65 Kept: 116688
% 175.26/175.65 Inuse: 1528
% 175.26/175.65 Deleted: 4512
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 419659
% 175.26/175.65 Kept: 119028
% 175.26/175.65 Inuse: 1552
% 175.26/175.65 Deleted: 4512
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying clauses:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 435009
% 175.26/175.65 Kept: 122887
% 175.26/175.65 Inuse: 1562
% 175.26/175.65 Deleted: 4776
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 444362
% 175.26/175.65 Kept: 125331
% 175.26/175.65 Inuse: 1572
% 175.26/175.65 Deleted: 4776
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 459352
% 175.26/175.65 Kept: 129501
% 175.26/175.65 Inuse: 1582
% 175.26/175.65 Deleted: 4776
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 474759
% 175.26/175.65 Kept: 133318
% 175.26/175.65 Inuse: 1592
% 175.26/175.65 Deleted: 4776
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 493123
% 175.26/175.65 Kept: 136850
% 175.26/175.65 Inuse: 1612
% 175.26/175.65 Deleted: 4776
% 175.26/175.65 Deletedinuse: 6
% 175.26/175.65
% 175.26/175.65 Resimplifying inuse:
% 175.26/175.65 Done
% 175.26/175.65
% 175.26/175.65
% 175.26/175.65 Intermediate Status:
% 175.26/175.65 Generated: 505Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------