TSTP Solution File: SWW260+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW260+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:39 EDT 2022
% Result : Timeout 300.05s 300.49s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWW260+1 : TPTP v8.1.0. Released v5.2.0.
% 0.00/0.10 % Command : bliksem %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % DateTime : Sat Jun 4 22:58:03 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.78/1.37 *** allocated 10000 integers for termspace/termends
% 0.78/1.37 *** allocated 10000 integers for clauses
% 0.78/1.37 *** allocated 10000 integers for justifications
% 0.78/1.37 *** allocated 15000 integers for termspace/termends
% 0.78/1.37 *** allocated 22500 integers for termspace/termends
% 0.78/1.37 *** allocated 33750 integers for termspace/termends
% 0.78/1.37 Bliksem 1.12
% 0.78/1.37
% 0.78/1.37
% 0.78/1.37 Automatic Strategy Selection
% 0.78/1.37
% 0.78/1.37 *** allocated 50625 integers for termspace/termends
% 0.78/1.37 *** allocated 75937 integers for termspace/termends
% 0.78/1.37 *** allocated 113905 integers for termspace/termends
% 0.78/1.37
% 0.78/1.37 Clauses:
% 0.78/1.37
% 0.78/1.37 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.78/1.37 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.78/1.37 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.78/1.37 tc_Complex_Ocomplex, v_p ) ) }.
% 0.78/1.37 { ! v_k____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, v_t____,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.78/1.37 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.78/1.37 c_RealVector_Oof__real( tc_Complex_Ocomplex, Y ) ), X ) =
% 0.78/1.37 c_RealVector_Oof__real( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.78/1.37 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.78/1.37 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.78/1.37 v_k____ ) ), c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_a____,
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.78/1.37 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.78/1.37 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.78/1.37 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 0.78/1.37 ) ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.78/1.37 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_k____ ) ),
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.78/1.37 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ),
% 0.78/1.37 v_k____ ) ), v_a____ ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.37 tc_Complex_Ocomplex ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.37 tc_Complex_Ocomplex ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.78/1.37 tc_Complex_Ocomplex ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.37 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.78/1.37 v_t____ ) ), v_w____ ) ), v_k____ ) ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.78/1.37 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ),
% 0.78/1.37 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.78/1.37 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 0.78/1.37 }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.78/1.37 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ),
% 0.78/1.37 v_k____ ) ), v_a____ ) = c_Groups_Ouminus__class_Ouminus(
% 0.78/1.37 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 0.78/1.37 .
% 0.78/1.37 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.78/1.37 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.37 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.78/1.37 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ), v_k____ )
% 0.78/1.37 ), v_a____ ) ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.78/1.37 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.78/1.37 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.78/1.37 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.78/1.37 .
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.78/1.37 c_Groups_Ominus__class_Ominus( X, c_RealVector_Oof__real( X, Z ),
% 0.78/1.37 c_RealVector_Oof__real( X, Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.78/1.37 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.78/1.37 c_Groups_Ominus__class_Ominus( X, c_RealVector_Oof__real( X, Z ),
% 0.78/1.37 c_RealVector_Oof__real( X, Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.78/1.37 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), Y ) )
% 0.78/1.37 = hAPP( hAPP( c_Power_Opower__class_Opower( X ), c_RealVector_Oof__real(
% 0.78/1.37 X, Z ) ), Y ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.78/1.37 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.37 , Y ) ) }.
% 0.78/1.37 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.78/1.37 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.78/1.37 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.78/1.37 X, Y ) ) }.
% 0.78/1.37 { ! v_a____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.78/1.37 { ! v_w____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_t____ ) }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ), v_k____ )
% 0.78/1.37 ), v_a____ ) ), c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }.
% 0.78/1.37 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.78/1.37 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.78/1.37 tc_Complex_Ocomplex, v_pa____ ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.78/1.37 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.78/1.37 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.78/1.37 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( X ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.78/1.37 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.78/1.37 , Z, Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.78/1.37 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.78/1.37 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), ! c_RealVector_Oof__real( X, Y
% 0.78/1.37 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_RealDef_Oreal ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), ! Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealVector_Oof__real(
% 0.78/1.37 X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.78/1.37 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , Y ) }.
% 0.78/1.37 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.78/1.37 , Y ) }.
% 0.78/1.37 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.78/1.37 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.78/1.37 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.78/1.37 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.78/1.37 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.78/1.37 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.78/1.37 .
% 0.78/1.37 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.78/1.37 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.78/1.37 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ) }.
% 0.78/1.37 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.78/1.37 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.78/1.37 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.78/1.37 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.37 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.78/1.37 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.37 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.78/1.37 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.78/1.37 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.37 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.78/1.37 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.78/1.37 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, Z, Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.78/1.37 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, Z, Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.78/1.37 , T ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.78/1.37 , T, Y ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.78/1.37 , Y, T ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.78/1.37 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, Z, Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.78/1.37 , T, Y ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.78/1.37 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, T, Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.78/1.37 , Y, Z ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.78/1.37 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.78/1.37 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.78/1.37 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.78/1.37 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.78/1.37 ( X, Y ), Z ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.78/1.37 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.78/1.37 ( X, Z ), Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.37 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.37 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.78/1.37 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.78/1.37 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.78/1.37 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.78/1.37 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.78/1.37 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.78/1.37 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.78/1.37 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.78/1.37 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.78/1.37 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.78/1.37 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.78/1.37 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.78/1.37 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.78/1.37 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.78/1.37 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.78/1.37 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.78/1.37 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.78/1.37 ) }.
% 0.78/1.37 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.78/1.37 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.78/1.37 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.78/1.37 tc_Nat_Onat ) ) = Y }.
% 0.78/1.37 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.78/1.37 tc_Nat_Onat ) ) = Y }.
% 0.78/1.37 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.78/1.37 = Y }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.78/1.37 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.78/1.37 ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.78/1.37 ) }.
% 0.78/1.37 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( X ) }.
% 0.78/1.37 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.37 , Y ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 = Y }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.78/1.37 ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( X ) }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.78/1.37 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.78/1.37 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.78/1.37 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.37 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.78/1.37 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 0.78/1.37 X, T ) = hAPP( X, U ) }.
% 0.78/1.37 { ! hAPP( X, skol2( X ) ) = hAPP( X, skol35( X ) ),
% 0.78/1.37 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Z, Y ) ) }.
% 0.78/1.37 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.78/1.37 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.78/1.37 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.78/1.37 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.78/1.37 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.37 Z ) = Y }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.78/1.37 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.78/1.37 ( X, Z ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.37 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.37 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.78/1.37 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.78/1.37 ( X, Y ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.37 X ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.78/1.37 X, Y ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.37 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.78/1.37 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.78/1.37 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 Y, T ), Z = Y }.
% 0.78/1.37 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 T, Y ), Z = Y }.
% 0.78/1.37 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 T, Y ), Z = Y }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.78/1.37 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.78/1.37 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.78/1.37 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 Y, Z ), T = Y }.
% 0.78/1.37 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 Y, Z ) }.
% 0.78/1.37 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 T, Y ), Z = Y }.
% 0.78/1.37 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 T, Y ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.78/1.37 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.78/1.37 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.78/1.37 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.78/1.37 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.78/1.37 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.78/1.37 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.78/1.37 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.78/1.37 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.78/1.37 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.78/1.37 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.78/1.37 c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.37 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.78/1.37 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.78/1.37 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.78/1.37 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.78/1.37 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.78/1.37 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.78/1.37 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.78/1.37 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.78/1.37 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.78/1.37 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.37 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.37 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), ! c_RealVector_Oof__real( X, Z
% 0.78/1.37 ) = c_RealVector_Oof__real( X, Y ), Z = Y }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), ! Z = Y,
% 0.78/1.37 c_RealVector_Oof__real( X, Z ) = c_RealVector_Oof__real( X, Y ) }.
% 0.78/1.37 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.78/1.37 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.78/1.37 ), U = Z, T = Y }.
% 0.78/1.37 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.78/1.37 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.78/1.37 ) }.
% 0.78/1.37 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.78/1.37 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.78/1.37 ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.78/1.37 ) ), Z ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.78/1.37 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.78/1.37 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.78/1.37 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.78/1.37 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.78/1.37 ) }.
% 0.78/1.37 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.78/1.37 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.78/1.37 ), ! U = T }.
% 0.78/1.37 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.78/1.37 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.78/1.37 ), ! Z = Y }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.37 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.78/1.37 = Y }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.78/1.37 = Y }.
% 0.78/1.37 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.78/1.37 = Y }.
% 0.78/1.37 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.78/1.37 = Y }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.78/1.37 = Y }.
% 0.78/1.37 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.78/1.37 = Y }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.78/1.37 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.78/1.37 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.78/1.37 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.78/1.37 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.78/1.37 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.78/1.37 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.78/1.37 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.78/1.37 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 Z, Y ) ) = Y }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.78/1.37 Y ) ) = Y }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.78/1.37 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.78/1.37 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.78/1.37 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.78/1.37 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.37 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.78/1.37 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.78/1.37 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.78/1.37 = c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) )
% 0.78/1.37 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), c_RealVector_Oof__real
% 0.78/1.37 ( X, Z ) ), c_RealVector_Oof__real( X, Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.78/1.37 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, c_RealVector_Oof__real( X, Z ),
% 0.78/1.37 c_RealVector_Oof__real( X, Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, c_RealVector_Oof__real( X, Z ),
% 0.78/1.37 c_RealVector_Oof__real( X, Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.78/1.37 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) =
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) =
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.78/1.37 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.78/1.37 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.78/1.37 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.78/1.37 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.78/1.37 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.78/1.37 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.78/1.37 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.78/1.37 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.78/1.37 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.78/1.37 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.78/1.37 Z ) ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.78/1.37 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.78/1.37 ) }.
% 0.78/1.37 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.78/1.37 X, Z, Y ) }.
% 0.78/1.37 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol3 ), v_k____ ) )
% 0.78/1.37 , v_a____ ) ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.78/1.37 { c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }.
% 0.78/1.37 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.78/1.37 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.37 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.78/1.37 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.78/1.37 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.78/1.37 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.78/1.37 X, W, Z ) ), U ), T ), Y ) }.
% 0.78/1.37 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), Z ), U ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.78/1.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.78/1.37 ( X, Z, W ) ), U ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.78/1.37 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.78/1.37 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.78/1.37 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.78/1.37 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.37 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.78/1.37 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.78/1.37 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.78/1.37 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.37 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.37 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.78/1.37 Z ) ), U ), T ) = Y }.
% 0.78/1.37 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.78/1.37 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), Z ), U ), Y ) }.
% 0.78/1.37 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.78/1.37 W ) ), U ), Y ) }.
% 0.78/1.37 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.78/1.37 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), Z ), U ), Y ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.78/1.37 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.78/1.37 ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_m____ ) }.
% 0.78/1.37 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.78/1.37 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex
% 0.78/1.37 , v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.78/1.37 }.
% 0.78/1.37 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.78/1.37 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.78/1.37 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.78/1.37 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.78/1.37 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.78/1.37 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.78/1.37 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.78/1.37 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.78/1.37 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.78/1.37 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.78/1.37 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.78/1.37 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.78/1.37 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.78/1.37 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.78/1.37 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.78/1.37 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.78/1.37 ), X ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.78/1.37 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.78/1.37 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.37 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.78/1.37 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.78/1.37 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, Y, Z ) }.
% 0.78/1.37 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.78/1.37 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.78/1.37 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.78/1.37 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.78/1.37 ( tc_Nat_Onat ) ) ) ) }.
% 0.78/1.37 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.37 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.37 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.37 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.37 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.78/1.37 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.78/1.37 ) ), T ), Y ) }.
% 0.78/1.37 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.78/1.37 ( X, Y ) ) }.
% 0.78/1.37 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.78/1.37 ) ), Y ) }.
% 0.78/1.37 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.78/1.37 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.78/1.37 ( X, Y ) ) }.
% 0.78/1.37 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.78/1.37 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.78/1.37 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.78/1.37 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.78/1.37 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.78/1.37 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.78/1.37 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.37 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.78/1.37 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.37 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.78/1.37 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( X ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.37 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.37 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.78/1.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.78/1.37 .
% 0.78/1.37 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.78/1.37 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.78/1.37 .
% 0.78/1.37 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.37 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.78/1.37 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( X ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.37 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.78/1.37 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( X ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.37 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.78/1.37 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.37 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.37 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha1( X, Y, Z, T ),
% 0.78/1.37 alpha12( X, Y, Z, T ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z, T ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha12( X, Y, Z, T ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.37 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.78/1.37 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha12( X, Y, Z, T ) }.
% 0.78/1.37 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.78/1.37 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.78/1.37 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha1( X, Y, Z, T ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha2( X, Y, Z, T ),
% 0.78/1.37 alpha13( X, Y, Z, T ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z, T ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha13( X, Y, Z, T ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.78/1.37 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha13( X, Y, Z, T ) }.
% 0.78/1.37 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.78/1.37 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.78/1.37 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha2( X, Y, Z, T ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.37 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.78/1.37 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.78/1.37 ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.37 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.78/1.37 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.78/1.37 ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.78/1.37 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.78/1.37 .
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.37 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.78/1.37 .
% 0.78/1.37 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.37 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.78/1.37 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.78/1.37 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.78/1.37 v_pa____ ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol4( Y ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol4( Y ),
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol4( X ), X ) }.
% 0.78/1.37 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.78/1.37 , alpha3( X, Y, Z ) }.
% 0.78/1.37 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.78/1.37 , alpha14( X, Y, Z ) }.
% 0.78/1.37 { ! alpha3( X, Y, Z ), ! alpha14( X, Y, Z ), hBOOL( hAPP( Z,
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.78/1.37 { ! alpha14( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.78/1.37 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.78/1.37 { ! hBOOL( hAPP( Z, skol5( T, U, Z ) ) ), alpha14( X, Y, Z ) }.
% 0.78/1.37 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol5( X, Y, Z ) ),
% 0.78/1.37 alpha14( X, Y, Z ) }.
% 0.78/1.37 { ! alpha3( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.78/1.37 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha3( X, Y, Z ) }.
% 0.78/1.37 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha3
% 0.78/1.37 ( X, Y, Z ) }.
% 0.78/1.37 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.78/1.37 , ! alpha4( X, Y, Z ) }.
% 0.78/1.37 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.78/1.37 , ! alpha15( X, Y, Z ) }.
% 0.78/1.37 { alpha4( X, Y, Z ), alpha15( X, Y, Z ), hBOOL( hAPP( Z,
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.78/1.37 { ! alpha15( X, Y, Z ), ! hBOOL( hAPP( Z, skol6( T, U, Z ) ) ) }.
% 0.78/1.37 { ! alpha15( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.78/1.37 skol6( X, Y, Z ) ) }.
% 0.78/1.37 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.78/1.37 ) ), alpha15( X, Y, Z ) }.
% 0.78/1.37 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.78/1.37 .
% 0.78/1.37 { ! alpha4( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ) ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha4( X, Y, Z ) }.
% 0.78/1.37 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.78/1.37 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Z, X ), Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.78/1.37 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.78/1.37 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.78/1.37 { ! class_Groups_Ozero( X ), !
% 0.78/1.37 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.37 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Polynomial_Opoly( X ) ),
% 0.78/1.37 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.78/1.37 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.78/1.37 { alpha19( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.78/1.37 ( X, Y ), Z ) ) }.
% 0.78/1.37 { ! alpha19( X, Y, Z ), alpha20( X, Y, Z ), Z = Y }.
% 0.78/1.37 { ! alpha19( X, Y, Z ), alpha20( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.78/1.37 ) ) }.
% 0.78/1.37 { ! alpha20( X, Y, Z ), alpha19( X, Y, Z ) }.
% 0.78/1.37 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha19( X, Y, Z ) }.
% 0.78/1.37 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.78/1.37 }.
% 0.78/1.37 { ! alpha20( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.78/1.37 X, Y ), Z ) ), alpha20( X, Y, Z ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.78/1.37 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.78/1.37 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.78/1.37 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.78/1.37 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.78/1.37 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.78/1.37 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.78/1.37 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.78/1.37 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.78/1.37 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.78/1.37 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.78/1.37 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.78/1.37 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.78/1.37 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), X ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.78/1.37 .
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), X ) }.
% 0.78/1.37 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), X ) = X }.
% 0.78/1.37 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ) ) = X }.
% 0.78/1.37 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.78/1.37 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.78/1.37 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.78/1.37 .
% 0.78/1.37 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.78/1.37 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.78/1.37 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.78/1.37 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.78/1.37 .
% 0.78/1.37 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.78/1.37 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.78/1.37 , X ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.78/1.37 .
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.78/1.37 .
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.78/1.37 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.78/1.37 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.78/1.37 .
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.78/1.37 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.78/1.37 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.78/1.37 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.78/1.37 ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.78/1.37 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.78/1.37 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.78/1.37 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.78/1.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.78/1.37 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.78/1.37 tc_Nat_Onat ) }.
% 0.78/1.37 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.78/1.37 tc_Nat_Onat ) }.
% 0.78/1.37 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.78/1.37 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.78/1.37 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.78/1.37 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.78/1.37 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.78/1.37 , Y ), X ) }.
% 0.78/1.37 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Y, X ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, Y, X ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.78/1.37 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.78/1.37 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.37 Y ), X ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), Z ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.78/1.37 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.78/1.37 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.78/1.37 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.78/1.37 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.78/1.37 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.37 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 0.78/1.37 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.78/1.37 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex, X
% 0.78/1.37 ), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.78/1.37 tc_Complex_Ocomplex, v_pa____ ) ),
% 0.78/1.37 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 0.78/1.37 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 0.78/1.37 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol7( X ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.78/1.37 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.78/1.37 skol8 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.78/1.37 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.78/1.37 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol8 ), X ) = hAPP(
% 0.78/1.37 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.78/1.37 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.78/1.37 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), skol9 ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.78/1.37 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.78/1.37 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.78/1.37 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, v_t____,
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.78/1.37 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), Y ) }.
% 0.78/1.37 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.78/1.37 ), X ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.78/1.37 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.78/1.37 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.78/1.37 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.78/1.37 tc_Complex_Ocomplex, v_q____ ) ) }.
% 0.78/1.37 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.78/1.37 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.78/1.37 tc_Complex_Ocomplex, v_q____ ) ) }.
% 0.78/1.37 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.78/1.37 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.78/1.37 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.78/1.37 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.78/1.37 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), X ) ), v_m____ ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 0.78/1.37 class_Rings_Odivision__ring__inverse__zero( X ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 0.78/1.37 Y ) ) = c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__div__algebra( X ), !
% 0.78/1.37 class_Rings_Odivision__ring__inverse__zero( X ), c_RealVector_Oof__real(
% 0.78/1.37 X, c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) =
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.78/1.37 , Y ) ) = Y }.
% 0.78/1.37 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.78/1.37 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__div__algebra( X ), Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ) ) =
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__div__algebra( X ), Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealVector_Oof__real(
% 0.78/1.37 X, c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) =
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.78/1.37 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.78/1.37 = Y }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.78/1.37 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( X ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.78/1.37 X, Y ) ) = Y }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.78/1.37 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.78/1.37 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.78/1.37 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.37 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.78/1.37 ) ), Y ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.78/1.37 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.78/1.37 ( X, Y, Z ) ) }.
% 0.78/1.37 { c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.78/1.37 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.78/1.37 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.78/1.37 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.37 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.78/1.37 ) ), Z ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.78/1.37 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.78/1.37 tc_RealDef_Oreal ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.78/1.37 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.78/1.37 ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.78/1.37 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.78/1.37 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), T ), hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ), Z ) ) }.
% 0.78/1.37 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.78/1.37 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.78/1.37 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), X ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10 ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol10,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol10,
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.78/1.37 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.78/1.37 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.78/1.37 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.78/1.37 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 0.78/1.37 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.78/1.37 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.78/1.37 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.78/1.37 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.78/1.37 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.78/1.37 c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.37 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.78/1.37 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.78/1.37 ) ) }.
% 0.78/1.37 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.78/1.37 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.78/1.37 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.37 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.78/1.37 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.37 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.78/1.37 tc_Complex_Ocomplex, v_s____ ), v_k____ ), c_Groups_Oone__class_Oone(
% 0.78/1.37 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.78/1.37 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.78/1.37 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.78/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.78/1.37 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.78/1.37 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.78/1.37 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.78/1.37 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.78/1.37 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.78/1.37 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.78/1.37 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.78/1.37 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.78/1.37 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.78/1.37 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.78/1.37 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.78/1.37 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.78/1.37 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.37 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.37 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.37 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.37 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.37 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.78/1.37 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.78/1.37 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.78/1.37 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.78/1.37 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.78/1.37 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.78/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.78/1.37 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.37 ) }.
% 0.78/1.37 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.37 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.78/1.37 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.78/1.37 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.78/1.37 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 ) }.
% 0.78/1.37 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.37 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.78/1.37 ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.78/1.37 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.78/1.37 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.37 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.78/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.78/1.37 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha5( X, Y
% 0.78/1.37 , Z ), alpha16( X, Y, Z ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.37 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.78/1.37 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ), alpha16( X, Y, Z ) }.
% 0.78/1.37 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.78/1.37 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Y ), alpha5( X, Y, Z ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( X ) ), alpha6( X, Y, Z ), alpha17( X, Y, Z ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( X ) ) }.
% 0.78/1.37 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z ),
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( X ) ) }.
% 0.78/1.37 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.78/1.37 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.78/1.37 ( X ), Y ), alpha17( X, Y, Z ) }.
% 0.78/1.37 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.78/1.37 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.37 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ), alpha6( X, Y, Z ) }.
% 0.78/1.37 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.37 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.78/1.37 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.78/1.37 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.78/1.37 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.37 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.37 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.37 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.78/1.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.37 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.37 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.78/1.37 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( X ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__semiring( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__semiring( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__semiring( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__semiring( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( X ) ) }.
% 0.78/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.78/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.78/1.38 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.78/1.38 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.78/1.38 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.78/1.38 Y, Z ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.78/1.38 Z, Y ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ) ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.78/1.38 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.78/1.38 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.78/1.38 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.78/1.38 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semidom( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Groups_Oone__class_Oone( X ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.78/1.38 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.78/1.38 , Y, T ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.78/1.38 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.78/1.38 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.78/1.38 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.78/1.38 , Y ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.78/1.38 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 0.78/1.38 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.78/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.78/1.38 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.38 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.78/1.38 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.38 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.78/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.78/1.38 ( X, Y ), Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.78/1.38 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.78/1.38 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.78/1.38 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.78/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.38 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.78/1.38 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.78/1.38 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.78/1.38 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 0.78/1.38 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.78/1.38 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.78/1.38 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.38 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.38 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.38 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.38 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.38 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.38 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.78/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.38 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.78/1.38 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.38 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.78/1.38 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.38 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.38 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.78/1.38 ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.78/1.38 ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.38 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.78/1.38 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.78/1.38 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.78/1.38 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.78/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.78/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.78/1.38 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.78/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.78/1.38 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.38 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.78/1.38 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.38 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.38 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.78/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.78/1.38 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.38 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.38 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.38 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.78/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.78/1.38 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.38 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.78/1.38 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.78/1.38 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.78/1.38 ( X, Y ) ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.78/1.38 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.78/1.38 ( X, Y ) ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.78/1.38 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.78/1.38 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.78/1.38 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.38 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.78/1.38 ), Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.78/1.38 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.78/1.38 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.78/1.38 ( X, T, Y ) ) ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.78/1.38 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.78/1.38 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.78/1.38 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.38 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.78/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.78/1.38 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.78/1.38 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.78/1.38 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.78/1.38 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.78/1.38 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.78/1.38 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.78/1.38 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.78/1.38 = c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.78/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.78/1.38 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.78/1.38 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.78/1.38 , Y ) ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.78/1.38 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( X ) ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.78/1.38 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol11 ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), X ) ), skol11 ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Y ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 0.78/1.38 Y ) ), c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Z ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.78/1.38 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.78/1.38 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.78/1.38 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.78/1.38 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.78/1.38 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.78/1.38 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.78/1.38 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.78/1.38 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.78/1.38 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.78/1.38 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.78/1.38 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.78/1.38 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.78/1.38 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 0.78/1.38 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.78/1.38 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.78/1.38 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.78/1.38 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.78/1.38 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 0.78/1.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ ) ),
% 0.78/1.38 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.78/1.38 tc_Complex_Ocomplex, v_a____, v_s____ ) ), X ) ) ) }.
% 0.78/1.38 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 0.78/1.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.78/1.38 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.78/1.38 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.78/1.38 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.78/1.38 v_q____ ) ), X ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.78/1.38 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 0.78/1.38 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) = hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.78/1.38 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.78/1.38 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.78/1.38 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.78/1.38 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), hAPP
% 0.78/1.38 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 0.78/1.38 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.78/1.38 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.78/1.38 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.78/1.38 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.78/1.38 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.78/1.38 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.78/1.38 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.78/1.38 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 0.78/1.38 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.78/1.38 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.78/1.38 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol12( X, Y ) ) }.
% 0.78/1.38 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.78/1.38 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.78/1.38 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol13( X, Y ) ) }.
% 0.78/1.38 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.78/1.38 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.38 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.78/1.38 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.78/1.38 ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.78/1.38 ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, Z, Y ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, Z, X ), Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.78/1.38 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.78/1.38 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.78/1.38 ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.78/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.78/1.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.78/1.38 ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.78/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.78/1.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.78/1.38 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex
% 0.78/1.38 , v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), c_Orderings_Oord__class_Oless
% 0.78/1.38 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.78/1.38 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.78/1.38 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.78/1.38 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.78/1.38 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.78/1.38 v_q____ ) ), skol14 ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.78/1.38 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.78/1.38 tc_Complex_Ocomplex, c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), c_Polynomial_Omonom(
% 0.78/1.38 tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 0.78/1.38 , v_k____, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) }.
% 0.78/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.78/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.78/1.38 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Complex_Ocomplex ), c_Polynomial_Omonom( tc_Complex_Ocomplex, v_a____
% 0.78/1.38 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) }.
% 0.78/1.38 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.78/1.38 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.78/1.38 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.78/1.38 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.78/1.38 v_q____ ) ), skol15 ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.78/1.38 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ),
% 0.78/1.38 skol36 ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.78/1.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.78/1.38 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.78/1.38 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.78/1.38 X, Z ), Y ) ) }.
% 0.78/1.38 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.78/1.38 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.78/1.38 c_Polynomial_Omonom( tc_Complex_Ocomplex, v_a____,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), skol16 ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.78/1.38 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.78/1.38 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.78/1.38 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.78/1.38 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.78/1.38 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.78/1.38 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.78/1.38 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.78/1.38 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.78/1.38 .
% 0.78/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.78/1.38 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.78/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.78/1.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.38 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.38 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.38 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.38 tc_Nat_Onat ), X ), Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.78/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.78/1.38 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.78/1.38 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.78/1.38 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.78/1.38 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.78/1.38 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.78/1.38 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.78/1.38 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.78/1.38 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.78/1.38 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.78/1.38 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.78/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), Y ) }.
% 0.78/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.78/1.38 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.78/1.38 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.78/1.38 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.78/1.38 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.78/1.38 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.78/1.38 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.78/1.38 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.78/1.38 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.78/1.38 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.78/1.38 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.78/1.38 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.78/1.38 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.78/1.38 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.78/1.38 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.78/1.38 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.78/1.38 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.78/1.38 c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.78/1.38 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.78/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.78/1.38 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.78/1.38 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.78/1.38 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.78/1.38 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.78/1.38 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.78/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.78/1.38 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.78/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.78/1.38 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.78/1.38 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.78/1.38 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.78/1.38 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.78/1.38 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.78/1.38 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.78/1.38 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.78/1.38 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.78/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.78/1.38 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.78/1.38 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.78/1.38 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.78/1.38 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.78/1.38 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.78/1.38 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.78/1.38 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.78/1.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.78/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.78/1.38 ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.78/1.38 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.78/1.38 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.78/1.38 , Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.78/1.38 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.78/1.38 Y ) ) }.
% 0.78/1.38 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.78/1.38 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.78/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.78/1.38 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.78/1.38 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.78/1.38 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.78/1.38 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.78/1.38 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.78/1.38 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.78/1.38 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.78/1.38 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.78/1.38 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.78/1.38 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.78/1.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.78/1.38 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.78/1.38 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.78/1.38 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.78/1.38 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.78/1.38 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.78/1.38 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.78/1.38 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.78/1.38 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol17( X, Y ) ), Y
% 0.78/1.38 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.78/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.78/1.38 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.78/1.38 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.78/1.38 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.78/1.38 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.78/1.38 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.78/1.38 , Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.78/1.38 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.78/1.38 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol18 ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), X ) ), skol18 ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.78/1.38 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.78/1.38 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.78/1.38 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.78/1.38 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.78/1.38 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.78/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.78/1.38 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 0.78/1.38 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.78/1.38 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! skol19 = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.78/1.38 { ! skol37 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.78/1.38 tc_Complex_Ocomplex, skol40 ), skol37 ), c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.78/1.38 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.78/1.38 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 0.78/1.38 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.78/1.38 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.78/1.38 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.78/1.38 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.78/1.38 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 0.78/1.38 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.78/1.38 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.78/1.38 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.78/1.38 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.78/1.38 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 0.78/1.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), skol37 ) ),
% 0.78/1.38 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.78/1.38 tc_Complex_Ocomplex, skol19, skol40 ) ), X ) ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.38 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.38 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.78/1.38 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.78/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.78/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.78/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.78/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.78/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.78/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.78/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.78/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.78/1.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.78/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.78/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.78/1.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.78/1.38 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.78/1.38 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.78/1.38 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.78/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.78/1.38 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.38 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 0.78/1.38 { c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, c_Complex_Oii ) =
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, c_Complex_Oii ) }.
% 0.78/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.78/1.38 c_Complex_Oii ), c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 0.78/1.38 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.78/1.38 , Y ) }.
% 0.78/1.38 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.78/1.38 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.78/1.38 class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol20( Y ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.78/1.38 class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol20( X ) ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.78/1.38 .
% 0.78/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Int_Oint ) ) = X }.
% 0.78/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Int_Oint ), X ) = X }.
% 0.78/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.78/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.78/1.38 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.78/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.78/1.38 .
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Int_Oint ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.78/1.38 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.78/1.38 .
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.78/1.38 ( tc_Int_Oint ) ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.78/1.38 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.78/1.38 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.78/1.38 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.78/1.38 ( tc_Int_Oint ) }.
% 0.78/1.38 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.78/1.38 = X }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Int_Oint ) ) ) }.
% 0.78/1.38 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Int_Oint ) ) ) }.
% 0.78/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.78/1.38 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.78/1.38 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.78/1.38 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.78/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.78/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.78/1.38 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.78/1.38 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Int_Oint ) ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.78/1.38 }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Int_Oint ) ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.78/1.38 }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Int_Oint ) ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.78/1.38 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.78/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.78/1.38 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.78/1.38 hAPP( Y, U ) ) }.
% 0.78/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.78/1.38 ( Z, skol21( X, Y, Z ) ), hAPP( Y, skol21( X, Y, Z ) ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.78/1.38 ( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.78/1.38 ( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.78/1.38 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.78/1.38 hAPP( Y, U ) ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.78/1.38 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.78/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.78/1.38 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.78/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.78/1.38 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.78/1.38 hAPP( Y, U ) ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.78/1.38 Y ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.78/1.38 Y ), ! Z = Y }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.78/1.38 Z ), ! Z = Y }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.78/1.38 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.78/1.38 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.78/1.38 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.78/1.38 , ! Z = Y }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.78/1.38 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.78/1.38 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.78/1.38 , ! Z = Y }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.78/1.38 , ! Y = Z }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.78/1.38 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.78/1.38 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.78/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.78/1.38 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.78/1.38 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.78/1.38 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.78/1.38 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.78/1.38 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.78/1.38 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.78/1.38 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.78/1.38 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.78/1.38 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.78/1.38 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.78/1.38 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.78/1.38 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.78/1.38 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.78/1.38 ( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.78/1.38 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.78/1.38 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.78/1.38 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.78/1.38 , ! Z = Y }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.78/1.38 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.78/1.38 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.78/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.78/1.38 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.78/1.38 ( tc_Int_Oint ), Y ) }.
% 0.78/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.78/1.38 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.78/1.38 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.78/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.78/1.38 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.78/1.38 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.78/1.38 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.78/1.38 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.78/1.38 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.78/1.38 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.78/1.38 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.78/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.78/1.38 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.78/1.38 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Int_Oint ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Int_Oint ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, X, Y ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.78/1.38 class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol22( Y ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.78/1.38 class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol22( X ) ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, T, skol23( X, U, W, T ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.78/1.38 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.78/1.38 ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.78/1.38 hAPP( Z, T ), hAPP( Z, skol23( X, Y, Z, T ) ) ) ),
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.78/1.38 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.78/1.38 ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol24( Z, T ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol24( X, Y ) ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25( Z, T ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol25( X, Y ) ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol26( Y ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol26( X ) ) ) }.
% 0.78/1.38 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.78/1.38 skol27 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.78/1.38 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.78/1.38 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol27 ), X ) = hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.78/1.38 tc_Int_Oint, X, Y ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.78/1.38 ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.78/1.38 ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.78/1.38 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.78/1.38 tc_Int_Oint, X, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.78/1.38 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha7
% 0.78/1.38 ( X, Y, Z ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.78/1.38 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! alpha7( X, Y, Z ),
% 0.78/1.38 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.78/1.38 { ! alpha7( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.78/1.38 ( X ) ) }.
% 0.78/1.38 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.78/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.78/1.38 alpha7( X, Y, Z ) }.
% 0.78/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.78/1.38 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.78/1.38 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.78/1.38 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.78/1.38 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.78/1.38 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.78/1.38 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol28( T, U, W ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ), skol28( X,
% 0.78/1.38 Y, Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), T ), hAPP(
% 0.78/1.38 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), Z ) ) ), X ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.78/1.38 tc_Nat_Onat, skol29( X, Y ), skol38( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.78/1.38 hAPP( Y, skol38( X, Y ) ), hAPP( Y, skol29( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.78/1.38 , Y ) }.
% 0.78/1.38 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.38 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.78/1.38 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.38 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.78/1.38 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.78/1.38 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.78/1.38 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.78/1.38 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.78/1.38 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.78/1.38 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.78/1.38 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.78/1.38 hAPP( Z, Y ) ) }.
% 0.78/1.38 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.78/1.38 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.78/1.38 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.78/1.38 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.78/1.38 ) ) }.
% 0.78/1.38 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.78/1.38 ( X, Y ), Z = Y }.
% 0.78/1.38 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.78/1.38 ( X, Y ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.78/1.38 class_RealVector_Oreal__normed__vector( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.78/1.38 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol30( X ) ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.78/1.38 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.78/1.38 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.78/1.38 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.78/1.38 ( X ) ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.78/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.38 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.78/1.38 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( X, c_RealVector_Oof__real( X, Y ) ) =
% 0.78/1.38 c_RealVector_Oof__real( X, c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, Y
% 0.78/1.38 ) ) }.
% 0.78/1.38 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.78/1.38 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.78/1.38 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.78/1.38 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.78/1.38 c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.78/1.38 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.78/1.38 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.78/1.38 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.78/1.38 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.38 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.78/1.38 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.78/1.38 c_Groups_Oone__class_Oone( X ) ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.78/1.38 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.78/1.38 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.78/1.38 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.78/1.38 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.78/1.38 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_RealDef_Oreal ) }.
% 0.78/1.38 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.78/1.38 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_RealDef_Oreal ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.78/1.38 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.78/1.38 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.78/1.38 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.78/1.38 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.78/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.78/1.38 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.78/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.78/1.38 c_Polynomial_OpCons( X, T,
% 0.78/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.78/1.38 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.78/1.38 , Y ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.78/1.38 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.78/1.38 , Z, Y ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.78/1.38 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.78/1.38 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.78/1.38 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.78/1.38 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.78/1.38 ), T ), U ), Y ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.78/1.38 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.78/1.38 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.78/1.38 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.78/1.38 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.78/1.38 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.78/1.38 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.78/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.78/1.38 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.78/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.78/1.38 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.78/1.38 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.78/1.38 X, T, Z ), Y ) }.
% 0.78/1.38 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.78/1.38 Z, T ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.78/1.38 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.78/1.38 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.78/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.78/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Polynomial_Opoly( X ) ),
% 0.78/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha8( X
% 0.78/1.38 , Y, T ) }.
% 0.78/1.38 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha18( X
% 0.78/1.38 , Y, Z, T ) }.
% 0.78/1.38 { ! class_Fields_Ofield( X ), ! alpha8( X, Y, T ), ! alpha18( X, Y, Z, T )
% 0.78/1.38 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.78/1.38 ( X, T, Z ), Y ) }.
% 0.78/1.38 { ! alpha18( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.78/1.38 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha18( X, Y, Z, T ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha18( X
% 0.78/1.38 , Y, Z, T ) }.
% 0.78/1.38 { ! alpha8( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { Z = c_Groups_Ozero__class_Ozero( X ), alpha8( X, Y, Z ) }.
% 0.78/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha8( X
% 0.78/1.38 , Y, Z ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.78/1.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.78/1.38 ( X ), Y ), Z ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.78/1.38 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.78/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.78/1.38 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.78/1.38 , Y ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.78/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.78/1.38 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.78/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Int_Oint ) }.
% 0.78/1.38 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.78/1.38 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Int_Oint ) ) }.
% 0.78/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.78/1.38 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.78/1.38 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.78/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.78/1.38 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.78/1.38 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.78/1.38 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.78/1.38 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.78/1.38 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.78/1.38 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.78/1.38 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.78/1.38 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.78/1.38 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.78/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.78/1.38 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.78/1.38 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.78/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.78/1.38 }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.78/1.38 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.78/1.38 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.78/1.38 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.78/1.38 .
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.78/1.38 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 0.78/1.38 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.78/1.38 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 0.78/1.38 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.78/1.38 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.78/1.38 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.78/1.38 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.78/1.38 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.78/1.38 , Z ), X ) ), T ) ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Int_Oint, U, T ) ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Int_Oint, Y, X ) }.
% 0.78/1.38 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.78/1.38 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.78/1.38 ) ) }.
% 0.78/1.38 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.78/1.38 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.78/1.38 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.78/1.38 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.78/1.38 X ) ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.78/1.38 ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.78/1.38 ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.78/1.38 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.78/1.38 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.78/1.38 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.78/1.38 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.78/1.38 ) }.
% 0.78/1.38 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.78/1.38 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.78/1.38 hAPP( Z, skol31( U, W, Z ) ) ) }.
% 0.78/1.38 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.78/1.38 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol31( X
% 0.78/1.38 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.78/1.38 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.78/1.38 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol39( X,
% 0.78/1.38 Y, Z ) ) ) ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.78/1.38 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.78/1.38 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.78/1.38 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.78/1.38 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.78/1.38 Y ) ) ), Y ) }.
% 0.78/1.38 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.78/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.78/1.38 Y ) ) ), Y ) }.
% 0.78/1.38 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.78/1.38 X ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.78/1.38 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.78/1.38 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.78/1.38 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha9( X, Y ), Y = X }
% 0.78/1.38 .
% 0.78/1.38 { ! alpha9( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! alpha9( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! alpha9( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), alpha9( X, Y ) }.
% 0.78/1.38 { ! alpha10( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! alpha10( X, Y ), ! Y = X }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha10( X, Y ) }
% 0.78/1.38 .
% 0.78/1.38 { ! alpha10( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! alpha10( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), alpha10( X, Y ) }.
% 0.78/1.38 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.78/1.38 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.78/1.38 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Nat_Onat, Y, Z ) }.
% 0.78/1.38 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Nat_Onat, Y, Z ) }.
% 0.78/1.38 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, Z, Y ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.78/1.38 , Z ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.78/1.38 Z, Y ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.78/1.38 tc_Nat_Onat, Y, Z ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, Z, Y ) }.
% 0.78/1.38 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.78/1.38 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.78/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.78/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.78/1.38 X ), Y ), Z = Y }.
% 0.78/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.78/1.38 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.78/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.78/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.78/1.38 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.78/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.78/1.38 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.78/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.78/1.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.78/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.78/1.38 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.78/1.38 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.78/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.78/1.38 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.78/1.38 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.78/1.38 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.78/1.38 .
% 0.78/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.78/1.38 ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.78/1.38 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.78/1.38 , c_Nat_OSuc( X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.78/1.38 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.78/1.38 }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.78/1.38 c_Nat_OSuc( X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.78/1.38 ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.78/1.38 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.78/1.38 ), X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.78/1.38 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.78/1.38 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.78/1.38 .
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.78/1.38 .
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.78/1.38 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.78/1.38 X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.78/1.38 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.78/1.38 }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 0.78/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.78/1.38 { ! alpha11( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.78/1.38 c_Nat_OSuc( X ) ) }.
% 0.78/1.38 { ! alpha11( X, Y ), Y = c_Nat_OSuc( skol32( Z, Y ) ) }.
% 0.78/1.38 { ! alpha11( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol32( X
% 0.78/1.38 , Y ), X ) }.
% 0.78/1.38 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.78/1.38 ), alpha11( X, Y ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.78/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.78/1.38 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol33( X ) ) }.
% 0.78/1.38 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.78/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol34( X, Y ) ) ) }.
% 0.78/1.38 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.78/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.78/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.78/1.38 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.78/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.78/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.78/1.38 ), X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.78/1.38 .
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.78/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.78/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.78/1.38 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.78/1.38 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.78/1.38 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.78/1.38 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.78/1.38 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.78/1.38 ) ) }.
% 0.78/1.38 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.78/1.38 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.78/1.38 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.38 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.78/1.38 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.78/1.38 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.78/1.38 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.78/1.38 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.78/1.38 ( tc_fun( Y, X ) ) }.
% 0.78/1.38 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.78/1.38 ) ) }.
% 0.78/1.38 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.78/1.38 .
% 0.78/1.38 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.78/1.38 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.78/1.38 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.78/1.38 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.78/1.38 tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.78/1.38 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.78/1.38 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.78/1.38 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.78/1.38 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.78/1.38 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.78/1.38 { class_Power_Opower( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.78/1.38 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.78/1.38 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.78/1.39 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.78/1.39 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.78/1.39 tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.78/1.39 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.78/1.39 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.78/1.39 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.78/1.39 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.78/1.39 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.78/1.39 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.78/1.39 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.78/1.39 tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.78/1.39 .
% 0.78/1.39 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_RealVector_Oreal__div__algebra( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_RealVector_Oreal__algebra__1( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 0.78/1.39 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.78/1.39 tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_RealVector_Oreal__div__algebra( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_RealVector_Oreal__algebra__1( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.78/1.39 { ! class_Rings_Oidom( X ),
% 0.78/1.39 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.78/1.39 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.78/1.39 ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.78/1.39 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.78/1.39 X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.78/1.39 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.78/1.39 ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.78/1.39 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.78/1.39 }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.78/1.39 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.78/1.39 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.78/1.39 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.78/1.39 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.78/1.39 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.78/1.39 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.78/1.39 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.78/1.39 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.78/1.39 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.78/1.39 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.78/1.39 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.78/1.39 ( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.78/1.39 ( tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.78/1.39 }.
% 0.78/1.39 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.78/1.39 ) ) }.
% 0.78/1.39 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.78/1.39 .
% 0.78/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.78/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.78/1.39 { ! c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.78/1.39 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.78/1.39 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.39 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.39 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.78/1.39 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_k____ ) ),
% 0.78/1.39 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex,
% 0.78/1.39 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ) ), hAPP( hAPP(
% 0.78/1.39 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.39 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.39 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.39 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.78/1.39 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.78/1.39 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.39 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.78/1.39 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.78/1.39 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.39 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.78/1.39 v_t____ ) ), v_w____ ) ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.78/1.39 tc_Complex_Ocomplex, c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.78/1.39 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.78/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.78/1.39 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 0.78/1.39 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.78/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.78/1.39 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.78/1.39 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.78/1.39 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 0.78/1.39 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.39 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.78/1.39 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.78/1.39 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.78/1.39 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.78/1.39 v_t____ ) ), v_w____ ) ) ) ) }.
% 0.78/1.39
% 0.78/1.39 *** allocated 15000 integers for clauses
% 0.78/1.39 *** allocated 22500 integers for clauses
% 0.78/1.39 *** allocated 33750 integers for clauses
% 0.78/1.39 *** allocated 50625 integers for clauses
% 0.78/1.39 *** allocated 75937 integers for clauses
% 0.78/1.39 percentage equality = 0.255524, percentage horn = 0.918667
% 0.78/1.39 This is a problem with some equality
% 0.78/1.39
% 0.78/1.39
% 0.78/1.39
% 0.78/1.39 Options Used:
% 0.78/1.39
% 0.78/1.39 useres = 1
% 0.78/1.39 useparamod = 1
% 0.78/1.39 useeqrefl = 1
% 0.78/1.39 useeqfact = 1
% 0.78/1.39 usefactor = 1
% 0.78/1.39 usesimpsplitting = 0
% 0.78/1.39 usesimpdemod = 5
% 0.78/1.39 usesimpres = 3
% 0.78/1.39
% 0.78/1.39 resimpinuse = 1000
% 0.78/1.39 resimpclauses = 20000
% 0.78/1.39 substype = eqrewr
% 0.78/1.39 backwardsubs = 1
% 0.78/1.39 selectoldest = 5
% 0.78/1.39
% 0.78/1.39 litorderings [0] = split
% 0.78/1.39 litorderings [1] = extend the termordering, first sorting on arguments
% 0.78/1.39
% 0.78/1.39 termordering = kbo
% 0.78/1.39
% 0.78/1.39 litapriori = 0
% 0.78/1.39 termapriori = 1
% 0.78/1.39 litaposteriori = 0
% 0.78/1.39 termaposteriori = 0
% 0.78/1.39 demodaposteriori = 0
% 0.78/1.39 ordereqreflfact = 0
% 0.78/1.39
% 0.78/1.39 litselect = negord
% 0.78/1.39
% 0.78/1.39 maxweight = 15
% 0.78/1.39 maxdepth = 30000
% 0.78/1.39 maxlength = 115
% 0.78/1.39 maxnrvars = 195
% 0.78/1.39 excuselevel = 1
% 0.78/1.39 increasemaxweight = 1
% 0.78/1.39
% 0.78/1.39 maxselected = 10000000
% 0.78/1.39 maxnrclauses = 10000000
% 0.78/1.39
% 0.78/1.39 showgenerated = 0
% 0.78/1.39 showkept = 0
% 0.78/1.39 showselected = 0
% 0.78/1.39 showdeleted = 0
% 0.78/1.39 showresimp = 1
% 0.78/1.39 showstatus = 2000
% 0.78/1.39
% 0.78/1.39 prologoutput = 0
% 0.78/1.39 nrgoals = 5000000
% 0.78/1.39 totalproof = 1
% 0.78/1.39
% 0.78/1.39 Symbols occurring in the translation:
% 0.78/1.39
% 0.78/1.39 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.78/1.39 . [1, 2] (w:1, o:219, a:1, s:1, b:0),
% 0.78/1.39 ! [4, 1] (w:0, o:126, a:1, s:1, b:0),
% 0.78/1.39 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.39 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.39 hAPP [38, 2] (w:1, o:243, a:1, s:1, b:0),
% 0.78/1.39 tc_Complex_Ocomplex [39, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.78/1.39 v_p [40, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.78/1.39 c_Polynomial_Opoly [41, 2] (w:1, o:244, a:1, s:1, b:0),
% 0.78/1.39 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [42, 3] (w:1, o:
% 0.78/1.39 268, a:1, s:1, b:0),
% 0.78/1.39 v_k____ [43, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.78/1.39 tc_Nat_Onat [44, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.78/1.39 c_Groups_Ozero__class_Ozero [45, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.78/1.39 tc_RealDef_Oreal [46, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.78/1.39 v_t____ [47, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.78/1.39 c_Groups_Oone__class_Oone [48, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.78/1.39 c_Orderings_Oord__class_Oless [49, 3] (w:1, o:269, a:1, s:1, b:0),
% 0.78/1.39 c_Power_Opower__class_Opower [52, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.78/1.39 c_RealVector_Oof__real [53, 2] (w:1, o:246, a:1, s:1, b:0),
% 0.78/1.39 c_Groups_Otimes__class_Otimes [54, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.78/1.39 v_w____ [55, 0] (w:1, o:52, a:1, s:1, b:0),
% 0.78/1.39 v_a____ [56, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.78/1.39 v_s____ [57, 0] (w:1, o:32, a:1, s:1, b:0),
% 0.78/1.39 c_Groups_Oplus__class_Oplus [58, 3] (w:1, o:271, a:1, s:1, b:0),
% 0.78/1.39 c_Groups_Ouminus__class_Ouminus [59, 2] (w:1, o:248, a:1, s:1, b:0),
% 0.78/1.39
% 0.78/1.39 class_Rings_Oring__1 [62, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.78/1.39 c_Groups_Ominus__class_Ominus [63, 3] (w:1, o:272, a:1, s:1, b:0),
% 0.78/1.39 class_RealVector_Oreal__algebra__1 [65, 1] (w:1, o:136, a:1, s:1, b:0
% 0.78/1.39 ),
% 0.78/1.39 class_RealVector_Oreal__normed__vector [66, 1] (w:1, o:137, a:1, s:1
% 0.78/1.39 , b:0),
% 0.78/1.39 class_Groups_Ogroup__add [68, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.78/1.39 class_Groups_Oab__group__add [69, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Ocomm__ring__1 [70, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.78/1.39 v_pa____ [71, 0] (w:1, o:63, a:1, s:1, b:0),
% 0.78/1.39 class_Groups_Ozero [73, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.78/1.39 class_Groups_Oordered__ab__group__add [75, 1] (w:1, o:146, a:1, s:1
% 0.78/1.39 , b:0),
% 0.78/1.39 class_Groups_Olinordered__ab__group__add [76, 1] (w:1, o:147, a:1, s:
% 0.78/1.39 1, b:0),
% 0.78/1.39 class_Power_Opower [81, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Omult__zero [82, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Ono__zero__divisors [83, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.78/1.39
% 0.78/1.39 class_Rings_Ozero__neq__one [84, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Olinordered__semidom [85, 1] (w:1, o:155, a:1, s:1, b:0)
% 0.78/1.39 ,
% 0.78/1.39 class_Groups_Oordered__comm__monoid__add [86, 1] (w:1, o:165, a:1, s:
% 0.78/1.39 1, b:0),
% 0.78/1.39 class_Groups_Oordered__ab__semigroup__add__imp__le [89, 1] (w:1, o:
% 0.78/1.39 166, a:1, s:1, b:0),
% 0.78/1.39 class_Groups_Oordered__cancel__ab__semigroup__add [91, 1] (w:1, o:167
% 0.78/1.39 , a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Ocomm__semiring__1 [96, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.78/1.39 class_Groups_Omonoid__mult [98, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.78/1.39 class_RealVector_Oreal__normed__algebra [99, 1] (w:1, o:172, a:1, s:1
% 0.78/1.39 , b:0),
% 0.78/1.39 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.78/1.39 100, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.78/1.39 class_Groups_Ocomm__monoid__add [101, 1] (w:1, o:191, a:1, s:1, b:0)
% 0.78/1.39 ,
% 0.78/1.39 class_Groups_Omonoid__add [102, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Oring__1__no__zero__divisors [103, 1] (w:1, o:173, a:1
% 0.78/1.39 , s:1, b:0),
% 0.78/1.39 class_Rings_Osemiring__0 [106, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.78/1.39 class_Groups_Oab__semigroup__mult [114, 1] (w:1, o:193, a:1, s:1, b:0
% 0.78/1.39 ),
% 0.78/1.39 class_Groups_Ocancel__semigroup__add [115, 1] (w:1, o:194, a:1, s:1
% 0.78/1.39 , b:0),
% 0.78/1.39 class_Groups_Ocancel__ab__semigroup__add [116, 1] (w:1, o:195, a:1
% 0.78/1.39 , s:1, b:0),
% 0.78/1.39 class_Groups_Oab__semigroup__add [117, 1] (w:1, o:196, a:1, s:1, b:0)
% 0.78/1.39 ,
% 0.78/1.39 class_Groups_Oone [118, 1] (w:1, o:197, a:1, s:1, b:0),
% 0.78/1.39 class_Groups_Ocomm__monoid__mult [125, 1] (w:1, o:198, a:1, s:1, b:0)
% 0.78/1.39 ,
% 0.78/1.39 class_Rings_Oring [126, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Oordered__ring [129, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Olinordered__ring__strict [130, 1] (w:1, o:153, a:1, s:1
% 0.78/1.39 , b:0),
% 0.78/1.39 class_Rings_Olinordered__ring [131, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.78/1.39 v_m____ [132, 0] (w:1, o:90, a:1, s:1, b:0),
% 0.78/1.39 v_c____ [133, 0] (w:1, o:91, a:1, s:1, b:0),
% 0.78/1.39 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [134, 2] (w:1, o:
% 0.78/1.39 247, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Olinordered__idom [140, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Oring__no__zero__divisors [141, 1] (w:1, o:175, a:1, s:1
% 0.78/1.39 , b:0),
% 0.78/1.39 class_Rings_Ocomm__semiring [142, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Osemiring [144, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Oidom [145, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Olinordered__comm__semiring__strict [146, 1] (w:1, o:157
% 0.78/1.39 , a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Olinordered__semiring__strict [147, 1] (w:1, o:158, a:1
% 0.78/1.39 , s:1, b:0),
% 0.78/1.39 hBOOL [151, 1] (w:1, o:199, a:1, s:1, b:0),
% 0.78/1.39 tc_Polynomial_Opoly [157, 1] (w:1, o:209, a:1, s:1, b:0),
% 0.78/1.39 v_q____ [162, 0] (w:1, o:104, a:1, s:1, b:0),
% 0.78/1.39 c_RealVector_Onorm__class_Onorm [165, 2] (w:1, o:245, a:1, s:1, b:0)
% 0.78/1.39 ,
% 0.78/1.39 c_Rings_Oinverse__class_Oinverse [166, 2] (w:1, o:249, a:1, s:1, b:0)
% 0.78/1.39 ,
% 0.78/1.39 c_Orderings_Oord__class_Oless__eq [167, 3] (w:1, o:273, a:1, s:1, b:0
% 0.78/1.39 ),
% 0.78/1.39 class_RealVector_Oreal__normed__div__algebra [168, 1] (w:1, o:181, a:
% 0.78/1.39 1, s:1, b:0),
% 0.78/1.39 class_Rings_Odivision__ring__inverse__zero [169, 1] (w:1, o:182, a:1
% 0.78/1.39 , s:1, b:0),
% 0.78/1.39 class_RealVector_Oreal__div__algebra [170, 1] (w:1, o:183, a:1, s:1
% 0.78/1.39 , b:0),
% 0.78/1.39 class_Rings_Odivision__ring [171, 1] (w:1, o:184, a:1, s:1, b:0),
% 0.78/1.39 class_RealVector_Oreal__normed__algebra__1 [172, 1] (w:1, o:185, a:1
% 0.78/1.39 , s:1, b:0),
% 0.78/1.39 class_Fields_Ofield [176, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.78/1.39 class_Fields_Olinordered__field [177, 1] (w:1, o:139, a:1, s:1, b:0)
% 0.78/1.39 ,
% 0.78/1.39 class_Fields_Olinordered__field__inverse__zero [178, 1] (w:1, o:140
% 0.78/1.39 , a:1, s:1, b:0),
% 0.78/1.39 c_Polynomial_Osmult [179, 3] (w:1, o:274, a:1, s:1, b:0),
% 0.78/1.39 class_Groups_Oordered__ab__semigroup__add [180, 1] (w:1, o:210, a:1
% 0.78/1.39 , s:1, b:0),
% 0.78/1.39 class_Rings_Oordered__cancel__semiring [181, 1] (w:1, o:186, a:1, s:1
% 0.78/1.39 , b:0),
% 0.78/1.39 class_Rings_Oordered__semiring [182, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.78/1.39
% 0.78/1.39 class_Rings_Oordered__comm__semiring [183, 1] (w:1, o:188, a:1, s:1
% 0.78/1.39 , b:0),
% 0.78/1.39 class_Rings_Olinordered__semiring [184, 1] (w:1, o:159, a:1, s:1, b:0
% 0.78/1.39 ),
% 0.78/1.39 class_Rings_Olinordered__semiring__1 [186, 1] (w:1, o:160, a:1, s:1
% 0.78/1.39 , b:0),
% 0.78/1.39 class_Rings_Olinordered__semiring__1__strict [187, 1] (w:1, o:161, a:
% 0.78/1.39 1, s:1, b:0),
% 0.78/1.39 class_Fields_Ofield__inverse__zero [188, 1] (w:1, o:141, a:1, s:1, b:
% 0.78/1.39 0),
% 0.78/1.39 c_Polynomial_OpCons [190, 3] (w:1, o:276, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Ocomm__semiring__0 [193, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.78/1.39
% 0.78/1.39 c_Polynomial_Omonom [195, 3] (w:1, o:277, a:1, s:1, b:0),
% 0.78/1.39 class_Int_Oring__char__0 [198, 1] (w:1, o:211, a:1, s:1, b:0),
% 0.78/1.39 class_Rings_Ocomm__ring [199, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.78/1.39 c_Polynomial_Osynthetic__div [200, 3] (w:1, o:278, a:1, s:1, b:0),
% 3.72/4.14 c_Polynomial_Opcompose [201, 3] (w:1, o:279, a:1, s:1, b:0),
% 3.72/4.14 tc_Int_Oint [202, 0] (w:1, o:114, a:1, s:1, b:0),
% 3.72/4.14 c_Complex_Oii [203, 0] (w:1, o:115, a:1, s:1, b:0),
% 3.72/4.14 c_Polynomial_Oorder [204, 3] (w:1, o:275, a:1, s:1, b:0),
% 3.72/4.14 class_Orderings_Opreorder [206, 1] (w:1, o:150, a:1, s:1, b:0),
% 3.72/4.14 c_Power_Opower_Opower [207, 3] (w:1, o:280, a:1, s:1, b:0),
% 3.72/4.14 class_Orderings_Oord [213, 1] (w:1, o:148, a:1, s:1, b:0),
% 3.72/4.14 tc_fun [214, 2] (w:1, o:260, a:1, s:1, b:0),
% 3.72/4.14 class_Orderings_Olinorder [215, 1] (w:1, o:151, a:1, s:1, b:0),
% 3.72/4.14 class_Orderings_Oorder [216, 1] (w:1, o:149, a:1, s:1, b:0),
% 3.72/4.14 c_Nat__Transfer_Otsub [222, 2] (w:1, o:261, a:1, s:1, b:0),
% 3.72/4.14 c_Polynomial_Opos__poly [223, 2] (w:1, o:262, a:1, s:1, b:0),
% 3.72/4.14 c_SEQ_Odecseq [224, 2] (w:1, o:263, a:1, s:1, b:0),
% 3.72/4.14 class_Lattices_Oboolean__algebra [225, 1] (w:1, o:213, a:1, s:1, b:0)
% 3.72/4.14 ,
% 3.72/4.14 class_Lattices_Oab__semigroup__idem__mult [226, 1] (w:1, o:212, a:1
% 3.72/4.14 , s:1, b:0),
% 3.72/4.14 class_Groups_Ominus [229, 1] (w:1, o:214, a:1, s:1, b:0),
% 3.72/4.14 class_Groups_Ouminus [230, 1] (w:1, o:215, a:1, s:1, b:0),
% 3.72/4.14 c_Groups_Osgn__class_Osgn [231, 2] (w:1, o:264, a:1, s:1, b:0),
% 3.72/4.14 class_Groups_Osgn__if [232, 1] (w:1, o:216, a:1, s:1, b:0),
% 3.72/4.14 c_Rings_Odvd__class_Odvd [233, 3] (w:1, o:281, a:1, s:1, b:0),
% 3.72/4.14 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [235, 3] (w:
% 3.72/4.14 1, o:270, a:1, s:1, b:0),
% 3.72/4.14 class_Rings_Odvd [236, 1] (w:1, o:189, a:1, s:1, b:0),
% 3.72/4.14 c_Nat_OSuc [240, 1] (w:1, o:217, a:1, s:1, b:0),
% 3.72/4.14 class_Groups_Ocancel__comm__monoid__add [243, 1] (w:1, o:218, a:1, s:
% 3.72/4.14 1, b:0),
% 3.72/4.14 tc_HOL_Obool [245, 0] (w:1, o:113, a:1, s:1, b:0),
% 3.72/4.14 alpha1 [246, 4] (w:1, o:300, a:1, s:1, b:1),
% 3.72/4.14 alpha2 [247, 4] (w:1, o:304, a:1, s:1, b:1),
% 3.72/4.14 alpha3 [248, 3] (w:1, o:283, a:1, s:1, b:1),
% 3.72/4.14 alpha4 [249, 3] (w:1, o:284, a:1, s:1, b:1),
% 3.72/4.14 alpha5 [250, 3] (w:1, o:285, a:1, s:1, b:1),
% 3.72/4.14 alpha6 [251, 3] (w:1, o:286, a:1, s:1, b:1),
% 3.72/4.14 alpha7 [252, 3] (w:1, o:287, a:1, s:1, b:1),
% 3.72/4.14 alpha8 [253, 3] (w:1, o:288, a:1, s:1, b:1),
% 3.72/4.14 alpha9 [254, 2] (w:1, o:265, a:1, s:1, b:1),
% 3.72/4.14 alpha10 [255, 2] (w:1, o:266, a:1, s:1, b:1),
% 3.72/4.14 alpha11 [256, 2] (w:1, o:267, a:1, s:1, b:1),
% 3.72/4.14 alpha12 [257, 4] (w:1, o:301, a:1, s:1, b:1),
% 3.72/4.14 alpha13 [258, 4] (w:1, o:302, a:1, s:1, b:1),
% 3.72/4.14 alpha14 [259, 3] (w:1, o:289, a:1, s:1, b:1),
% 3.72/4.14 alpha15 [260, 3] (w:1, o:290, a:1, s:1, b:1),
% 3.72/4.14 alpha16 [261, 3] (w:1, o:291, a:1, s:1, b:1),
% 3.72/4.14 alpha17 [262, 3] (w:1, o:292, a:1, s:1, b:1),
% 3.72/4.14 alpha18 [263, 4] (w:1, o:303, a:1, s:1, b:1),
% 3.72/4.14 alpha19 [264, 3] (w:1, o:293, a:1, s:1, b:1),
% 3.72/4.14 alpha20 [265, 3] (w:1, o:282, a:1, s:1, b:1),
% 3.72/4.14 skol1 [266, 2] (w:1, o:250, a:1, s:1, b:1),
% 3.72/4.14 skol2 [267, 1] (w:1, o:200, a:1, s:1, b:1),
% 3.72/4.14 skol3 [268, 0] (w:1, o:14, a:1, s:1, b:1),
% 3.72/4.14 skol4 [269, 1] (w:1, o:204, a:1, s:1, b:1),
% 3.72/4.14 skol5 [270, 3] (w:1, o:294, a:1, s:1, b:1),
% 3.72/4.14 skol6 [271, 3] (w:1, o:295, a:1, s:1, b:1),
% 3.72/4.14 skol7 [272, 1] (w:1, o:205, a:1, s:1, b:1),
% 3.72/4.14 skol8 [273, 0] (w:1, o:15, a:1, s:1, b:1),
% 3.72/4.14 skol9 [274, 0] (w:1, o:16, a:1, s:1, b:1),
% 3.72/4.14 skol10 [275, 0] (w:1, o:17, a:1, s:1, b:1),
% 3.72/4.14 skol11 [276, 0] (w:1, o:18, a:1, s:1, b:1),
% 3.72/4.14 skol12 [277, 2] (w:1, o:251, a:1, s:1, b:1),
% 3.72/4.14 skol13 [278, 2] (w:1, o:252, a:1, s:1, b:1),
% 3.72/4.14 skol14 [279, 0] (w:1, o:19, a:1, s:1, b:1),
% 3.72/4.14 skol15 [280, 0] (w:1, o:20, a:1, s:1, b:1),
% 3.72/4.14 skol16 [281, 0] (w:1, o:21, a:1, s:1, b:1),
% 3.72/4.14 skol17 [282, 2] (w:1, o:253, a:1, s:1, b:1),
% 3.72/4.14 skol18 [283, 0] (w:1, o:22, a:1, s:1, b:1),
% 3.72/4.14 skol19 [284, 0] (w:1, o:23, a:1, s:1, b:1),
% 3.72/4.14 skol20 [285, 1] (w:1, o:206, a:1, s:1, b:1),
% 3.72/4.14 skol21 [286, 3] (w:1, o:296, a:1, s:1, b:1),
% 3.72/4.14 skol22 [287, 1] (w:1, o:207, a:1, s:1, b:1),
% 3.72/4.14 skol23 [288, 4] (w:1, o:305, a:1, s:1, b:1),
% 3.72/4.14 skol24 [289, 2] (w:1, o:254, a:1, s:1, b:1),
% 3.72/4.14 skol25 [290, 2] (w:1, o:255, a:1, s:1, b:1),
% 27.02/27.40 skol26 [291, 1] (w:1, o:208, a:1, s:1, b:1),
% 27.02/27.40 skol27 [292, 0] (w:1, o:13, a:1, s:1, b:1),
% 27.02/27.40 skol28 [293, 3] (w:1, o:297, a:1, s:1, b:1),
% 27.02/27.40 skol29 [294, 2] (w:1, o:256, a:1, s:1, b:1),
% 27.02/27.40 skol30 [295, 1] (w:1, o:201, a:1, s:1, b:1),
% 27.02/27.40 skol31 [296, 3] (w:1, o:298, a:1, s:1, b:1),
% 27.02/27.40 skol32 [297, 2] (w:1, o:257, a:1, s:1, b:1),
% 27.02/27.40 skol33 [298, 1] (w:1, o:202, a:1, s:1, b:1),
% 27.02/27.40 skol34 [299, 2] (w:1, o:258, a:1, s:1, b:1),
% 27.02/27.40 skol35 [300, 1] (w:1, o:203, a:1, s:1, b:1),
% 27.02/27.40 skol36 [301, 0] (w:1, o:24, a:1, s:1, b:1),
% 27.02/27.40 skol37 [302, 0] (w:1, o:25, a:1, s:1, b:1),
% 27.02/27.40 skol38 [303, 2] (w:1, o:259, a:1, s:1, b:1),
% 27.02/27.40 skol39 [304, 3] (w:1, o:299, a:1, s:1, b:1),
% 27.02/27.40 skol40 [305, 0] (w:1, o:26, a:1, s:1, b:1).
% 27.02/27.40
% 27.02/27.40
% 27.02/27.40 Starting Search:
% 27.02/27.40
% 27.02/27.40 *** allocated 113905 integers for clauses
% 27.02/27.40 *** allocated 170857 integers for clauses
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40
% 27.02/27.40 Intermediate Status:
% 27.02/27.40 Generated: 3076
% 27.02/27.40 Kept: 2000
% 27.02/27.40 Inuse: 87
% 27.02/27.40 Deleted: 2
% 27.02/27.40 Deletedinuse: 0
% 27.02/27.40
% 27.02/27.40 *** allocated 256285 integers for clauses
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 *** allocated 170857 integers for termspace/termends
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 *** allocated 384427 integers for clauses
% 27.02/27.40
% 27.02/27.40 Intermediate Status:
% 27.02/27.40 Generated: 7019
% 27.02/27.40 Kept: 4024
% 27.02/27.40 Inuse: 228
% 27.02/27.40 Deleted: 3
% 27.02/27.40 Deletedinuse: 0
% 27.02/27.40
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 *** allocated 256285 integers for termspace/termends
% 27.02/27.40
% 27.02/27.40 Intermediate Status:
% 27.02/27.40 Generated: 10483
% 27.02/27.40 Kept: 6091
% 27.02/27.40 Inuse: 318
% 27.02/27.40 Deleted: 3
% 27.02/27.40 Deletedinuse: 0
% 27.02/27.40
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 *** allocated 576640 integers for clauses
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40
% 27.02/27.40 Intermediate Status:
% 27.02/27.40 Generated: 14147
% 27.02/27.40 Kept: 8483
% 27.02/27.40 Inuse: 368
% 27.02/27.40 Deleted: 3
% 27.02/27.40 Deletedinuse: 0
% 27.02/27.40
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 *** allocated 384427 integers for termspace/termends
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 *** allocated 864960 integers for clauses
% 27.02/27.40
% 27.02/27.40 Intermediate Status:
% 27.02/27.40 Generated: 17908
% 27.02/27.40 Kept: 11224
% 27.02/27.40 Inuse: 408
% 27.02/27.40 Deleted: 3
% 27.02/27.40 Deletedinuse: 0
% 27.02/27.40
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40
% 27.02/27.40 Intermediate Status:
% 27.02/27.40 Generated: 21022
% 27.02/27.40 Kept: 13393
% 27.02/27.40 Inuse: 433
% 27.02/27.40 Deleted: 3
% 27.02/27.40 Deletedinuse: 0
% 27.02/27.40
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 *** allocated 576640 integers for termspace/termends
% 27.02/27.40
% 27.02/27.40 Intermediate Status:
% 27.02/27.40 Generated: 25067
% 27.02/27.40 Kept: 15586
% 27.02/27.40 Inuse: 472
% 27.02/27.40 Deleted: 4
% 27.02/27.40 Deletedinuse: 0
% 27.02/27.40
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 *** allocated 1297440 integers for clauses
% 27.02/27.40
% 27.02/27.40 Intermediate Status:
% 27.02/27.40 Generated: 39904
% 27.02/27.40 Kept: 18418
% 27.02/27.40 Inuse: 496
% 27.02/27.40 Deleted: 5
% 27.02/27.40 Deletedinuse: 0
% 27.02/27.40
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 Resimplifying clauses:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40
% 27.02/27.40 Intermediate Status:
% 27.02/27.40 Generated: 43623
% 27.02/27.40 Kept: 20435
% 27.02/27.40 Inuse: 524
% 27.02/27.40 Deleted: 350
% 27.02/27.40 Deletedinuse: 0
% 27.02/27.40
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40
% 27.02/27.40 Intermediate Status:
% 27.02/27.40 Generated: 47254
% 27.02/27.40 Kept: 22517
% 27.02/27.40 Inuse: 546
% 27.02/27.40 Deleted: 350
% 27.02/27.40 Deletedinuse: 0
% 27.02/27.40
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40 *** allocated 864960 integers for termspace/termends
% 27.02/27.40 Resimplifying inuse:
% 27.02/27.40 Done
% 27.02/27.40
% 27.02/27.40
% 27.02/27.40 Intermediate Status:
% 27.02/27.40 Generated: 55168
% 27.02/27.41 Kept: 25266
% 27.02/27.41 Inuse: 581
% 27.02/27.41 Deleted: 350
% 27.02/27.41 Deletedinuse: 0
% 27.02/27.41
% 27.02/27.41 Resimplifying inuse:
% 27.02/27.41 Done
% 27.02/27.41
% 27.02/27.41 Resimplifying inuse:
% 27.02/27.41 Done
% 27.02/27.41
% 27.02/27.41 *** allocated 1946160 integers for clauses
% 27.02/27.41
% 27.02/27.41 Intermediate Status:
% 27.02/27.41 Generated: 63880
% 27.02/27.41 Kept: 27958
% 27.02/27.41 Inuse: 591
% 27.02/27.41 Deleted: 350
% 27.02/27.41 Deletedinuse: 0
% 27.02/27.41
% 27.02/27.41 Resimplifying inuse:
% 27.02/27.41 Done
% 27.02/27.41
% 27.02/27.41 Resimplifying inuse:
% 27.02/27.41 Done
% 27.02/27.41
% 27.02/27.41
% 27.02/27.41 Intermediate Status:
% 27.02/27.41 Generated: 70402
% 27.02/27.41 Kept: 30909
% 27.02/27.41 Inuse: 631
% 27.02/27.41 Deleted: 350
% 27.02/27.41 Deletedinuse: 0
% 27.02/27.41
% 27.02/27.41 Resimplifying inuse:
% 27.02/27.41 Done
% 27.02/27.41
% 27.02/27.41 Resimplifying inuse:
% 27.02/27.41 Done
% 27.02/27.41
% 27.02/27.41
% 27.02/27.41 Intermediate Status:
% 27.02/27.41 Generated: 79455
% 27.02/27.41 Kept: 34196
% 27.02/27.41 Inuse: 646
% 27.02/27.41 Deleted: 350
% 27.02/27.41 Deletedinuse: 0
% 27.02/27.41
% 27.02/27.41 Resimplifying inuse:
% 27.02/27.41 Done
% 27.02/27.41
% 27.02/27.41 Resimplifying inuse:
% 27.02/27.41 Done
% 27.02/27.41
% 27.02/27.41
% 27.02/27.41 Intermediate Status:
% 27.02/27.41 Generated: 85630
% 27.02/27.41 Kept: 36210
% 27.02/27.41 Inuse: 662
% 27.02/27.41 Deleted: 350
% 27.02/27.41 Deletedinuse: 0
% 27.02/27.41
% 27.02/27.41 *** allocated 1297440 integers for termspace/termends
% 27.02/27.41
% 27.02/27.41 Intermediate Status:
% 27.02/27.41 Generated: 103369
% 27.02/27.41 Kept: 38511
% 27.02/27.41 Inuse: 666
% 27.02/27.41 Deleted: 350
% 27.02/27.41 Deletedinuse: 0
% 27.02/27.41
% 27.02/27.41 Resimplifying inuse:
% 27.02/27.41 Done
% 27.02/27.41
% 27.02/27.41 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying clauses:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 110690
% 93.81/94.18 Kept: 40659
% 93.81/94.18 Inuse: 691
% 93.81/94.18 Deleted: 448
% 93.81/94.18 Deletedinuse: 0
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 *** allocated 2919240 integers for clauses
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 115996
% 93.81/94.18 Kept: 42668
% 93.81/94.18 Inuse: 724
% 93.81/94.18 Deleted: 448
% 93.81/94.18 Deletedinuse: 0
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 121412
% 93.81/94.18 Kept: 44668
% 93.81/94.18 Inuse: 758
% 93.81/94.18 Deleted: 448
% 93.81/94.18 Deletedinuse: 0
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 126982
% 93.81/94.18 Kept: 46709
% 93.81/94.18 Inuse: 791
% 93.81/94.18 Deleted: 448
% 93.81/94.18 Deletedinuse: 0
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 134053
% 93.81/94.18 Kept: 48950
% 93.81/94.18 Inuse: 816
% 93.81/94.18 Deleted: 448
% 93.81/94.18 Deletedinuse: 0
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 141122
% 93.81/94.18 Kept: 50987
% 93.81/94.18 Inuse: 845
% 93.81/94.18 Deleted: 448
% 93.81/94.18 Deletedinuse: 0
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 *** allocated 1946160 integers for termspace/termends
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 149731
% 93.81/94.18 Kept: 52993
% 93.81/94.18 Inuse: 862
% 93.81/94.18 Deleted: 450
% 93.81/94.18 Deletedinuse: 2
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 154485
% 93.81/94.18 Kept: 55089
% 93.81/94.18 Inuse: 876
% 93.81/94.18 Deleted: 450
% 93.81/94.18 Deletedinuse: 2
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 161461
% 93.81/94.18 Kept: 57623
% 93.81/94.18 Inuse: 891
% 93.81/94.18 Deleted: 450
% 93.81/94.18 Deletedinuse: 2
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 167350
% 93.81/94.18 Kept: 59646
% 93.81/94.18 Inuse: 902
% 93.81/94.18 Deleted: 450
% 93.81/94.18 Deletedinuse: 2
% 93.81/94.18
% 93.81/94.18 *** allocated 4378860 integers for clauses
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 176474
% 93.81/94.18 Kept: 61807
% 93.81/94.18 Inuse: 906
% 93.81/94.18 Deleted: 450
% 93.81/94.18 Deletedinuse: 2
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying clauses:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 186880
% 93.81/94.18 Kept: 64354
% 93.81/94.18 Inuse: 921
% 93.81/94.18 Deleted: 1110
% 93.81/94.18 Deletedinuse: 2
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 194046
% 93.81/94.18 Kept: 66416
% 93.81/94.18 Inuse: 941
% 93.81/94.18 Deleted: 1110
% 93.81/94.18 Deletedinuse: 2
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 198186
% 93.81/94.18 Kept: 69030
% 93.81/94.18 Inuse: 946
% 93.81/94.18 Deleted: 1110
% 93.81/94.18 Deletedinuse: 2
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 *** allocated 2919240 integers for termspace/termends
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 208966
% 93.81/94.18 Kept: 74053
% 93.81/94.18 Inuse: 966
% 93.81/94.18 Deleted: 1112
% 93.81/94.18 Deletedinuse: 4
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 220299
% 93.81/94.18 Kept: 77299
% 93.81/94.18 Inuse: 981
% 93.81/94.18 Deleted: 1112
% 93.81/94.18 Deletedinuse: 4
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 241319
% 93.81/94.18 Kept: 79674
% 93.81/94.18 Inuse: 986
% 93.81/94.18 Deleted: 1112
% 93.81/94.18 Deletedinuse: 4
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 271692
% 93.81/94.18 Kept: 83604
% 93.81/94.18 Inuse: 996
% 93.81/94.18 Deleted: 1112
% 93.81/94.18 Deletedinuse: 4
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying clauses:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 288588
% 93.81/94.18 Kept: 87166
% 93.81/94.18 Inuse: 1003
% 93.81/94.18 Deleted: 1283
% 93.81/94.18 Deletedinuse: 4
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 296402
% 93.81/94.18 Kept: 89263
% 93.81/94.18 Inuse: 1016
% 93.81/94.18 Deleted: 1283
% 93.81/94.18 Deletedinuse: 4
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 304797
% 93.81/94.18 Kept: 91271
% 93.81/94.18 Inuse: 1044
% 93.81/94.18 Deleted: 1283
% 93.81/94.18 Deletedinuse: 4
% 93.81/94.18
% 93.81/94.18 *** allocated 6568290 integers for clauses
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 317085
% 93.81/94.18 Kept: 94162
% 93.81/94.18 Inuse: 1061
% 93.81/94.18 Deleted: 1283
% 93.81/94.18 Deletedinuse: 4
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 333543
% 93.81/94.18 Kept: 97099
% 93.81/94.18 Inuse: 1081
% 93.81/94.18 Deleted: 1284
% 93.81/94.18 Deletedinuse: 5
% 93.81/94.18
% 93.81/94.18 Resimplifying inuse:
% 93.81/94.18 Done
% 93.81/94.18
% 93.81/94.18
% 93.81/94.18 Intermediate Status:
% 93.81/94.18 Generated: 353147
% 93.81/94.18 Kept: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------