TSTP Solution File: SWW276+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW276+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 23:21:46 EDT 2022
% Result : Timeout 300.08s 300.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW276+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Mon Jun 6 05:02:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.98/1.59 *** allocated 10000 integers for termspace/termends
% 0.98/1.59 *** allocated 10000 integers for clauses
% 0.98/1.59 *** allocated 10000 integers for justifications
% 0.98/1.59 *** allocated 15000 integers for termspace/termends
% 0.98/1.59 *** allocated 22500 integers for termspace/termends
% 0.98/1.59 *** allocated 33750 integers for termspace/termends
% 0.98/1.59 Bliksem 1.12
% 0.98/1.59
% 0.98/1.59
% 0.98/1.59 Automatic Strategy Selection
% 0.98/1.59
% 0.98/1.59 *** allocated 50625 integers for termspace/termends
% 0.98/1.59 *** allocated 75937 integers for termspace/termends
% 0.98/1.59 *** allocated 113905 integers for termspace/termends
% 0.98/1.59
% 0.98/1.59 Clauses:
% 0.98/1.59
% 0.98/1.59 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.98/1.59 { ! v_n = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! v_na____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ) ) }.
% 0.98/1.59 { ! c_Polynomial_Odegree( tc_Complex_Ocomplex, v_s____ ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) = v_n }.
% 0.98/1.59 { ! c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! v_pa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ) ) }.
% 0.98/1.59 { ! v_s____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ) ) }.
% 0.98/1.59 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_pa____ ) = v_na____ }.
% 0.98/1.59 { v_pa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.98/1.59 ( tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.59 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.98/1.59 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.98/1.59 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.98/1.59 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 0.98/1.59 , v_s____ ) }.
% 0.98/1.59 { v_qa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.98/1.59 ( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.98/1.59 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ) ) ) ) ), v_r____ ) }.
% 0.98/1.59 { v_pa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.98/1.59 ( tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.59 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.98/1.59 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.98/1.59 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.98/1.59 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 0.98/1.59 , skol2 ) }.
% 0.98/1.59 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 0.98/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.98/1.59 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 0.98/1.59 v_a____, v_pa____ ) ), v_pa____ ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.98/1.59 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.98/1.59 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.98/1.59 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.98/1.59 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.59 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.59 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.59 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ), v_pa____, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.98/1.59 ( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_qa____ ), v_na____ ) )
% 0.98/1.59 }.
% 0.98/1.59 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 0.98/1.59 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( tc_Complex_Ocomplex, v_a____ ), c_Polynomial_OpCons(
% 0.98/1.59 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.98/1.59 ) ), v_qa____ ) }.
% 0.98/1.59 { ! c_Polynomial_Odegree( tc_Complex_Ocomplex, v_s____ ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.59 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), v_pa____, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.98/1.59 ), v_qa____ ), v_na____ ) ) }.
% 0.98/1.59 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_a____ ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.59 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_qa____ ), X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.59 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.98/1.59 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.59 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.98/1.59 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.98/1.59 .
% 0.98/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.98/1.59 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.98/1.59 .
% 0.98/1.59 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.98/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Nat_Onat ) ) = Y }.
% 0.98/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.59 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.98/1.59 c_Polynomial_Odegree( X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.98/1.59 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.98/1.59 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.59 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.59 ), X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.98/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.98/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), Z ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.59 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.59 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.59 Y ), X ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.59 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.98/1.59 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.98/1.59 ( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.98/1.59 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.59 { alpha47( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.98/1.59 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.59 { alpha47( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.98/1.59 ( X, Y ), Z ) ) }.
% 0.98/1.59 { ! alpha47( X, Y, Z ), alpha50( X, Y, Z ), Z = Y }.
% 0.98/1.59 { ! alpha47( X, Y, Z ), alpha50( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.98/1.59 ) ) }.
% 0.98/1.59 { ! alpha50( X, Y, Z ), alpha47( X, Y, Z ) }.
% 0.98/1.59 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha47( X, Y, Z ) }.
% 0.98/1.59 { ! alpha50( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.98/1.59 }.
% 0.98/1.59 { ! alpha50( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.98/1.59 X, Y ), Z ) ), alpha50( X, Y, Z ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.59 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.59 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.98/1.59 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.98/1.59 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.98/1.59 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.98/1.59 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.98/1.59 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.98/1.59 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.59 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.98/1.59 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.98/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ) }.
% 0.98/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.59 = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.98/1.59 .
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.98/1.59 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.98/1.59 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.59 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.59 .
% 0.98/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.59 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ) }.
% 0.98/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.59 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.98/1.59 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.59 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.59 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.98/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.98/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.59 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { v_qa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.98/1.59 ( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.98/1.59 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ) ) ) ) ), skol3 ) }.
% 0.98/1.59 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 0.98/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.98/1.59 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.59 tc_Complex_Ocomplex ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder(
% 0.98/1.59 tc_Complex_Ocomplex, v_a____, v_pa____ ) ) ), v_pa____ ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Oorder(
% 0.98/1.59 tc_Complex_Ocomplex, X, v_pa____ ), v_na____ ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), ! hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, Z ), skol4( T, Z ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.98/1.59 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.59 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.98/1.59 ), Z ), X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol4( Y, Z ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.98/1.59 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.59 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.98/1.59 ), Z ), X ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.98/1.59 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.98/1.59 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.98/1.59 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.59 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.98/1.59 }.
% 0.98/1.59 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.98/1.59 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.59 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.98/1.59 }.
% 0.98/1.59 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.98/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.59 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.98/1.59 }.
% 0.98/1.59 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.98/1.59 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.59 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.98/1.59 }.
% 0.98/1.59 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.59 X ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! X = c_Nat_OSuc( X ) }.
% 0.98/1.59 { ! c_Nat_OSuc( X ) = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.98/1.59 .
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.98/1.59 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.59 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.59 , Y ), X ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.98/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.59 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.98/1.59 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.98/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.98/1.59 ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.98/1.59 , c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.98/1.59 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.98/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.98/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.98/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.98/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.98/1.59 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.98/1.59 }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.98/1.59 c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Nat_Onat ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Nat_Onat ) }.
% 0.98/1.59 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.98/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.98/1.59 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.59 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.98/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.59 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.59 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.59 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.59 ), X ) ) }.
% 0.98/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.98/1.59 ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.98/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.98/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.98/1.59 ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.98/1.59 .
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Y ), Z = Y }.
% 0.98/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.98/1.59 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.98/1.59 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 0.98/1.59 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.98/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.98/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.98/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.98/1.59 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.98/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.98/1.59 }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.98/1.59 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.59 X ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.98/1.59 .
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.98/1.59 .
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.98/1.59 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.98/1.59 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.59 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.59 ), X ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.59 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha1( X, Y
% 0.98/1.59 , Z ), alpha19( X, Y, Z ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), alpha19( X, Y, Z ) }.
% 0.98/1.59 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.59 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ), alpha1( X, Y, Z ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ) ), alpha2( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ) ) }.
% 0.98/1.59 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ), Y ), alpha20( X, Y, Z ) }.
% 0.98/1.59 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.59 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), alpha2( X, Y, Z ) }.
% 0.98/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.98/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.98/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.59 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.59 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.98/1.60 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.60 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.60 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.98/1.60 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol5( X ) ) }.
% 0.98/1.60 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha3( X, Y ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.60 { ! alpha3( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.60 c_Nat_OSuc( X ) ) }.
% 0.98/1.60 { ! alpha3( X, Y ), Y = c_Nat_OSuc( skol6( Z, Y ) ) }.
% 0.98/1.60 { ! alpha3( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol6( X, Y
% 0.98/1.60 ), X ) }.
% 0.98/1.60 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.98/1.60 ), alpha3( X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.98/1.60 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.98/1.60 ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.98/1.60 ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.60 ), T ), U ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.60 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.60 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.98/1.60 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.98/1.60 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.60 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.98/1.60 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.98/1.60 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.98/1.60 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, Z ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.98/1.60 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.60 Z, T ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Nat_Onat ) ) = Y }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.60 ( X ), Z, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X )
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree
% 0.98/1.60 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.98/1.60 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.98/1.60 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.60 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.98/1.60 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.60 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.98/1.60 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.60 ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.60 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.60 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.60 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.98/1.60 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.60 , Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.60 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.98/1.60 , Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.60 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.98/1.60 Y ) ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.60 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.98/1.60 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.98/1.60 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.98/1.60 Y ) ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha4( X, Y, Z, T ),
% 0.98/1.60 alpha21( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha21( X, Y, Z, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha21( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.60 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha4( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha5( X, Y, Z, T ),
% 0.98/1.60 alpha22( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha22( X, Y, Z, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha22( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.98/1.60 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha5( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.60 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.60 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.98/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.98/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.98/1.60 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.60 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Y ) }.
% 0.98/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.60 ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.98/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha6( X, Y ), Y = X }
% 0.98/1.60 .
% 0.98/1.60 { ! alpha6( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! alpha6( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! alpha6( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), alpha6( X, Y ) }.
% 0.98/1.60 { ! alpha7( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! alpha7( X, Y ), ! Y = X }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha7( X, Y ) }
% 0.98/1.60 .
% 0.98/1.60 { ! alpha7( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! alpha7( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), alpha7( X, Y ) }.
% 0.98/1.60 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.98/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.98/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.98/1.60 , Z ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.98/1.60 Z, Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.98/1.60 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.60 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.60 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.60 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.60 = Y }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.60 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ), Z ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Z ), Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.98/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.98/1.60 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.60 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.60 X ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ), Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , Y ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.60 , Y ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.98/1.60 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Nat_Onat, Z, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Y ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.98/1.60 c_Polynomial_Odegree( X, Y ) ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.98/1.60 , Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.98/1.60 hAPP( Y, U ) ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.98/1.60 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.98/1.60 hAPP( Y, U ) ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.98/1.60 hAPP( Y, U ) ) }.
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.98/1.60 ( Z, skol7( X, Y, Z ) ), hAPP( Y, skol7( X, Y, Z ) ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), ! Z = Y }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 Z ), ! Z = Y }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , ! Z = Y }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , ! Z = Y }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , ! Y = Z }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.98/1.60 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Int_Oint, Z, X ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.98/1.60 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), !
% 0.98/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , ! Z = Y }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.60 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.98/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ) ) }.
% 0.98/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Nat_Onat ), X ) }.
% 0.98/1.60 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.98/1.60 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 0.98/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.60 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.98/1.60 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha8
% 0.98/1.60 ( X, Y, Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.60 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! alpha8( X, Y, Z ),
% 0.98/1.60 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.98/1.60 { ! alpha8( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.60 alpha8( X, Y, Z ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.98/1.60 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.98/1.60 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.60 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.98/1.60 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.98/1.60 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.98/1.60 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.60 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.60 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.60 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.98/1.60 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.98/1.60 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.98/1.60 X, Z ), Y ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.98/1.60 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.98/1.60 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.98/1.60 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.98/1.60 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.60 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.98/1.60 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.98/1.60 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.60 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.98/1.60 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ), Z = Y }.
% 0.98/1.60 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.98/1.60 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Int_Oint, Y, X ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.98/1.60 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.98/1.60 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.98/1.60 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.98/1.60 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.98/1.60 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 0.98/1.60 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 0.98/1.60 , Y ) }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.98/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.98/1.60 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.98/1.60 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.98/1.60 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.98/1.60 hAPP( Z, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.98/1.60 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.98/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.98/1.60 ( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.98/1.60 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.60 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.60 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.98/1.60 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.98/1.60 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.98/1.60 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.98/1.60 c_Polynomial_Ocoeff( X, Y ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.98/1.60 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol8( X
% 0.98/1.60 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol8( X, Y, Z ) ), Z = Y
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.60 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.60 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.98/1.60 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.98/1.60 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.60 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.60 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.60 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.60 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.60 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.60 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.98/1.60 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.98/1.60 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.60 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.60 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.98/1.60 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 0.98/1.60 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.60 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ) ) = Z }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.60 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.98/1.60 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.60 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.60 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.98/1.60 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.60 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.98/1.60 ) ) = X }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.60 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.60 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.60 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.98/1.60 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.98/1.60 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.60 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.98/1.60 ( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.98/1.60 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.98/1.60 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.60 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.60 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.98/1.60 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.98/1.60 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.98/1.60 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.98/1.60 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.98/1.60 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.98/1.60 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.60 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.98/1.60 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.98/1.60 ) ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.98/1.60 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.98/1.60 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.98/1.60 ( tc_Int_Oint ) ) ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.98/1.60 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.98/1.60 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.98/1.60 .
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.98/1.60 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.98/1.60 , skol9( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Polynomial_Odegree( X, Y ), Z ) }.
% 0.98/1.60 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol9( X
% 0.98/1.60 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.98/1.60 Y ), Z ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.60 Y ) ) = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 Z, Y ) ) = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.98/1.60 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.60 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.60 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.98/1.60 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.98/1.60 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 Y, T ), Z = Y }.
% 0.98/1.60 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 T, Y ), Z = Y }.
% 0.98/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 T, Y ), Z = Y }.
% 0.98/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 Y, Z ), T = Y }.
% 0.98/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 Y, Z ) }.
% 0.98/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 T, Y ), Z = Y }.
% 0.98/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 T, Y ) }.
% 0.98/1.60 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.60 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.60 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.60 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.60 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.60 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.60 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.60 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.60 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.60 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.60 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.60 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.98/1.60 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.60 ), U = Z, T = Y }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.98/1.60 ) ), T ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.98/1.60 ) ), Z ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.60 ), ! U = T }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.60 ), ! Z = Y }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.60 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.60 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.60 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , Y, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , T, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , Y, T ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , T, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.60 , T ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 Z, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 Y, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.60 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.60 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , Y, T ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 Z ) = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Z ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( X, Y ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.60 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.60 W ) ), U ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.60 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), U ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.60 Z ) ), U ), T ) = Y }.
% 0.98/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.60 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), U ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.60 Z ) ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.60 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.60 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.60 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.60 X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.98/1.60 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.98/1.60 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.60 , Y ) ) }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.98/1.60 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.98/1.60 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.98/1.60 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.98/1.60 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.60 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.60 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.60 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.60 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.60 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.60 X, W, Z ) ), U ), T ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), U ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( X, Z, W ) ), U ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.60 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.98/1.60 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.98/1.60 hAPP( Z, skol10( U, W, Z ) ) ) }.
% 0.98/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.98/1.60 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol10( X
% 0.98/1.60 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.98/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.98/1.60 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol28( X,
% 0.98/1.60 Y, Z ) ) ) ) }.
% 0.98/1.60 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.60 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.98/1.60 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.98/1.60 ), Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.98/1.60 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.98/1.60 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.98/1.60 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.98/1.60 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.60 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.60 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.60 , alpha33( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha33( X, Y, Z, T ),
% 0.98/1.60 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.98/1.60 { ! alpha33( X, Y, Z, T ), alpha9( X, Z, T ) }.
% 0.98/1.60 { ! alpha33( X, Y, Z, T ), alpha23( X, Y, T ) }.
% 0.98/1.60 { ! alpha9( X, Z, T ), ! alpha23( X, Y, T ), alpha33( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha23( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), alpha34( X, Y, Z ) }.
% 0.98/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha23( X
% 0.98/1.60 , Y, Z ) }.
% 0.98/1.60 { ! alpha34( X, Y, Z ), alpha23( X, Y, Z ) }.
% 0.98/1.60 { ! alpha34( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha34( X
% 0.98/1.60 , Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.98/1.60 ), c_Polynomial_Odegree( X, Z ) ), alpha34( X, Y, Z ) }.
% 0.98/1.60 { ! alpha9( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X, Y
% 0.98/1.60 , Z ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X
% 0.98/1.60 , Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Int_Oint, X, Y ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.60 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.98/1.60 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.98/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.60 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.98/1.60 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.60 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol11( X, Y ) ) }.
% 0.98/1.60 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ) ) = X }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), X ) = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.98/1.60 , X ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), X ) = X }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ) ) = X }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.98/1.60 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.98/1.60 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.60 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.60 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ) ) }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha10( X, Y ), alpha24( X
% 0.98/1.60 , Y ) }.
% 0.98/1.60 { ! alpha10( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! alpha24( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! alpha24( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! alpha24( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha24( X, Y ) }.
% 0.98/1.60 { ! alpha10( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! alpha10( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 0.98/1.60 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha11( X, Y ),
% 0.98/1.60 alpha25( X, Y ) }.
% 0.98/1.60 { ! alpha11( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.60 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! alpha25( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.60 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! alpha25( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! alpha25( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha25( X, Y ) }.
% 0.98/1.60 { ! alpha11( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! alpha11( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, X, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol12( X, Y ) ) ) }.
% 0.98/1.60 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.98/1.60 .
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.98/1.60 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.98/1.60 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.98/1.60 = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Int_Oint ) ) ) }.
% 0.98/1.60 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Int_Oint ) ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.98/1.60 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.98/1.60 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.98/1.60 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.98/1.60 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.98/1.60 , Z ), X ) ), T ) ) }.
% 0.98/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.98/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, U, T ) ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.98/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.60 , ! alpha12( X, Y, Z ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.61 , ! alpha26( X, Y, Z ) }.
% 0.98/1.61 { alpha12( X, Y, Z ), alpha26( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.61 { ! alpha26( X, Y, Z ), ! hBOOL( hAPP( Z, skol13( T, U, Z ) ) ) }.
% 0.98/1.61 { ! alpha26( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.61 skol13( X, Y, Z ) ) }.
% 0.98/1.61 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.98/1.61 ) ), alpha26( X, Y, Z ) }.
% 0.98/1.61 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.98/1.61 }.
% 0.98/1.61 { ! alpha12( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12( X, Y, Z ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.61 , alpha13( X, Y, Z ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.61 , alpha27( X, Y, Z ) }.
% 0.98/1.61 { ! alpha13( X, Y, Z ), ! alpha27( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.61 { ! alpha27( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.61 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, skol14( T, U, Z ) ) ), alpha27( X, Y, Z ) }.
% 0.98/1.61 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol14( X, Y, Z ) ),
% 0.98/1.61 alpha27( X, Y, Z ) }.
% 0.98/1.61 { ! alpha13( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.98/1.61 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha13( X, Y, Z ) }
% 0.98/1.61 .
% 0.98/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13
% 0.98/1.61 ( X, Y, Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.98/1.61 }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.98/1.61 }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.98/1.61 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.98/1.61 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.61 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.98/1.61 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.98/1.61 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 0.98/1.61 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.98/1.61 c_Polynomial_Odegree( X, Z ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.61 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.98/1.61 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.98/1.61 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.98/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.98/1.61 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.61 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.98/1.61 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.98/1.61 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.98/1.61 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.98/1.61 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.98/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.98/1.61 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.98/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.98/1.61 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.98/1.61 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.98/1.61 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.61 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.98/1.61 tc_Int_Oint, X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.98/1.61 ( tc_Int_Oint ), Y ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.98/1.61 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.98/1.61 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.61 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.98/1.61 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.61 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.98/1.61 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.61 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.61 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol15( X, Y ) ) }.
% 0.98/1.61 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.61 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.98/1.61 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 0.98/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.98/1.61 , Z ) ) }.
% 0.98/1.61 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.98/1.61 , Z ) ) }.
% 0.98/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.61 ( tc_Int_Oint, Y ), X ) }.
% 0.98/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.61 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.61 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.98/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.61 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.61 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 0.98/1.61 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.61 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.98/1.61 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 0.98/1.61 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.98/1.61 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.61 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.98/1.61 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.61 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 }.
% 0.98/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.98/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.61 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.98/1.61 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.98/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.61 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.98/1.61 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.61 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.98/1.61 , Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.98/1.61 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.98/1.61 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha14( X, Y ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.61 { ! alpha14( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.61 { ! alpha14( X, Y ), alpha28( X, Y ), alpha35( X, Y ) }.
% 0.98/1.61 { ! alpha28( X, Y ), alpha14( X, Y ) }.
% 0.98/1.61 { ! alpha35( X, Y ), alpha14( X, Y ) }.
% 0.98/1.61 { ! alpha35( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! alpha35( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha35( X, Y ) }.
% 0.98/1.61 { ! alpha28( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.98/1.61 { ! alpha28( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha28( X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, X, Y ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, Z, Y ), X ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.98/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.98/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.98/1.61 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.98/1.61 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.98/1.61 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.98/1.61 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 0.98/1.61 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 0.98/1.61 ( X, Z, Y ) = T }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.98/1.61 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 0.98/1.61 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 0.98/1.61 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.98/1.61 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 0.98/1.61 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.98/1.61 alpha15( X, Z ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.98/1.61 alpha29( X, Y, Z ) }.
% 0.98/1.61 { ! alpha15( X, Z ), ! alpha29( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.98/1.61 { ! alpha29( X, Y, Z ), alpha36( X, Y, Z ) }.
% 0.98/1.61 { ! alpha29( X, Y, Z ), alpha39( X, Y, Z ) }.
% 0.98/1.61 { ! alpha36( X, Y, Z ), ! alpha39( X, Y, Z ), alpha29( X, Y, Z ) }.
% 0.98/1.61 { ! alpha39( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha42( X, Y, Z ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha39( X, Y, Z ) }.
% 0.98/1.61 { ! alpha42( X, Y, Z ), alpha39( X, Y, Z ) }.
% 0.98/1.61 { ! alpha42( X, Y, Z ), ! alpha44( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, skol16( T, U, Z ) ) ), alpha42( X, Y, Z ) }.
% 0.98/1.61 { alpha44( X, Y, skol16( X, Y, Z ) ), alpha42( X, Y, Z ) }.
% 0.98/1.61 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 skol17( X, T, U ) ) }.
% 0.98/1.61 { ! alpha44( X, Y, Z ), alpha46( X, Y, Z, skol17( X, Y, Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha46( X, Y, Z
% 0.98/1.61 , T ), alpha44( X, Y, Z ) }.
% 0.98/1.61 { ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! alpha46( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha46( X,
% 0.98/1.61 Y, Z, T ) }.
% 0.98/1.61 { ! alpha36( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha40( X, Y, Z ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), X ), alpha36( X, Y, Z ) }.
% 0.98/1.61 { ! alpha40( X, Y, Z ), alpha36( X, Y, Z ) }.
% 0.98/1.61 { ! alpha40( X, Y, Z ), ! alpha43( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, skol18( T, U, Z ) ) ), alpha40( X, Y, Z ) }.
% 0.98/1.61 { alpha43( X, Y, skol18( X, Y, Z ) ), alpha40( X, Y, Z ) }.
% 0.98/1.61 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol19( T, U, W ) ) }.
% 0.98/1.61 { ! alpha43( X, Y, Z ), alpha45( X, Y, Z, skol19( X, Y, Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha45( X, Y, Z, T )
% 0.98/1.61 , alpha43( X, Y, Z ) }.
% 0.98/1.61 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.98/1.61 ) }.
% 0.98/1.61 { ! alpha45( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha45( X,
% 0.98/1.61 Y, Z, T ) }.
% 0.98/1.61 { ! alpha15( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.61 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha15( X, Y ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha15
% 0.98/1.61 ( X, Y ) }.
% 0.98/1.61 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha48( X,
% 0.98/1.61 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, T, Z ) = Y }.
% 0.98/1.61 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha48( X,
% 0.98/1.61 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Int_Oint, T, Z ) = Y }.
% 0.98/1.61 { ! alpha48( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.98/1.61 { ! alpha48( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha48( X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.98/1.61 , alpha48( X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.98/1.61 ( tc_Int_Oint, X, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.98/1.61 ( X ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.98/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.61 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.98/1.61 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.98/1.61 ( X ), T, Z ), Y ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.98/1.61 ( X ), Z, Y ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.98/1.61 ( X ), Z, Y ) ) }.
% 0.98/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.98/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.61 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.98/1.61 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.98/1.61 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.98/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.98/1.61 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.61 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.98/1.61 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.61 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.98/1.61 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.61 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.98/1.61 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.61 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.98/1.61 alpha16( X, Z ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.98/1.61 alpha30( X, Y, Z ) }.
% 0.98/1.61 { ! alpha16( X, Z ), ! alpha30( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.61 { ! alpha30( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 alpha37( X, Y, Z ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha30( X, Y, Z ) }.
% 0.98/1.61 { ! alpha37( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.98/1.61 { ! alpha37( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.98/1.61 ), alpha41( X, Y, Z, T ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol20( X, T, U ), X ),
% 0.98/1.61 alpha37( X, Y, Z ) }.
% 0.98/1.61 { ! alpha41( X, Y, Z, skol20( X, Y, Z ) ), alpha37( X, Y, Z ) }.
% 0.98/1.61 { ! alpha41( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.98/1.61 hBOOL( hAPP( Z, U ) ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Z, skol21( U, W, Z, V0 ) ) ), alpha41( X, Y, Z, T ) }.
% 0.98/1.61 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol21( X, Y, Z, T ) )
% 0.98/1.61 , T ), alpha41( X, Y, Z, T ) }.
% 0.98/1.61 { ! alpha16( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha16( X, Y ) }.
% 0.98/1.61 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16
% 0.98/1.61 ( X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ),
% 0.98/1.61 ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ), Z
% 0.98/1.61 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.98/1.61 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.98/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.98/1.61 alpha17( X, Z ), alpha31( X, Y, Z ) }.
% 0.98/1.61 { ! alpha17( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.61 { ! alpha31( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.98/1.61 tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.61 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol22( X
% 0.98/1.61 , Y, T ) ), Y ) }.
% 0.98/1.61 { ! alpha31( X, Y, Z ), alpha38( X, Y, Z, skol22( X, Y, Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ), Y ), ! alpha38( X
% 0.98/1.61 , Y, Z, T ), alpha31( X, Y, Z ) }.
% 0.98/1.61 { ! alpha38( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 0.98/1.61 ( T ) ) ) }.
% 0.98/1.61 { ! alpha38( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 0.98/1.61 hBOOL( hAPP( Z, T ) ), alpha38( X, Y, Z, T ) }.
% 0.98/1.61 { ! alpha17( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! alpha17( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) ) ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17( X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.98/1.61 , Y ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.61 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.98/1.61 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.61 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.98/1.61 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol23( Z, Y ) ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.98/1.61 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.98/1.61 tc_Int_Oint, skol23( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.61 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.98/1.61 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.98/1.61 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.98/1.61 , Z ), X ) ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol24( Z, Y ) ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.98/1.61 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Int_Oint, skol24( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.61 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.98/1.61 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.98/1.61 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.98/1.61 ) ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.61 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Int_Oint ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.98/1.61 tc_Int_Oint ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.98/1.61 .
% 0.98/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.98/1.61 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol25( Z, Y
% 0.98/1.61 ), Y ) }.
% 0.98/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.98/1.61 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.61 skol25( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.98/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.98/1.61 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.98/1.61 , skol25( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.61 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.61 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Z, Y ), alpha51( X, Y, Z, T ), ! Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.61 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Z, Y ), alpha51( X, Y, Z, T ), ! hAPP(
% 0.98/1.61 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.98/1.61 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.98/1.61 .
% 0.98/1.61 { ! alpha51( X, Y, Z, T ), alpha52( X, Y, Z, T ), alpha49( X, Y, T ) }.
% 0.98/1.61 { ! alpha51( X, Y, Z, T ), alpha52( X, Y, Z, T ), ! hAPP(
% 0.98/1.61 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! alpha52( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 0.98/1.61 { ! alpha49( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.98/1.61 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.61 alpha51( X, Y, Z, T ) }.
% 0.98/1.61 { ! alpha52( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.61 ( X ), Z, T ), alpha53( X, Y, Z, T ) }.
% 0.98/1.61 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha52( X, Y
% 0.98/1.61 , Z, T ) }.
% 0.98/1.61 { ! alpha53( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 0.98/1.61 { ! alpha53( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.98/1.61 ), skol26( X, Y, U, W ), Y ) }.
% 0.98/1.61 { ! alpha53( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.98/1.61 ), skol26( X, Y, U, T ), T ) }.
% 0.98/1.61 { ! alpha53( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.61 ( X ), skol26( X, Y, Z, T ), Z ) }.
% 0.98/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 0.98/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha53( X, Y
% 0.98/1.61 , Z, T ) }.
% 0.98/1.61 { ! alpha49( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! alpha49( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha49( X, Y, Z
% 0.98/1.61 ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha18( X, Y, T,
% 0.98/1.61 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha18( X, Y, skol27( X, Y
% 0.98/1.61 , Z ), skol29( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.98/1.61 skol27( X, Y, Z ) ), skol29( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.98/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.98/1.61 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.98/1.61 ) }.
% 0.98/1.61 { ! alpha18( X, Y, Z, T ), alpha32( X, Y, Z, T ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha32( X, Y, Z
% 0.98/1.61 , T ), alpha18( X, Y, Z, T ) }.
% 0.98/1.61 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.61 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.61 { ! alpha32( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha32( X,
% 0.98/1.61 Y, Z, T ) }.
% 0.98/1.61 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.61 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.61 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.98/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.61 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.61 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.61 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.98/1.61 tc_Int_Oint, Y, X ), X ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.61 ( X, Z, Y ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.98/1.61 ( X, Y, Z ) }.
% 0.98/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.98/1.61 , Y ) ), Y ) }.
% 0.98/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.98/1.61 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.61 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.98/1.61 ( tc_fun( Y, X ) ) }.
% 0.98/1.61 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.98/1.61 ) ) }.
% 0.98/1.61 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.98/1.61 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.98/1.61 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.98/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.61 tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.98/1.61 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.98/1.61 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.98/1.61 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.98/1.61 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.98/1.61 { class_Power_Opower( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.98/1.61 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.98/1.61 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.98/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.61 tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.98/1.61 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.98/1.61 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.98/1.61 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.98/1.61 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.98/1.61 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.98/1.61 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.98/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.61 tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ),
% 0.98/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.98/1.61 ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.98/1.61 X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.98/1.61 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.98/1.61 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.98/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.98/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.98/1.61 ( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.98/1.61 ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.98/1.61 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), c_Polynomial_Odegree( tc_Complex_Ocomplex, v_s____ ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____,
% 0.98/1.61 v_pa____ ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.98/1.61 tc_Complex_Ocomplex, v_s____ ), c_Polynomial_Odegree( tc_Complex_Ocomplex
% 0.98/1.61 , v_pa____ ) ) }.
% 0.98/1.61
% 0.98/1.61 *** allocated 15000 integers for clauses
% 0.98/1.61 *** allocated 22500 integers for clauses
% 0.98/1.61 *** allocated 33750 integers for clauses
% 0.98/1.61 *** allocated 50625 integers for clauses
% 0.98/1.61 *** allocated 75937 integers for clauses
% 0.98/1.61 percentage equality = 0.265063, percentage horn = 0.899543
% 0.98/1.61 This is a problem with some equality
% 0.98/1.61
% 0.98/1.61
% 0.98/1.61
% 0.98/1.61 Options Used:
% 0.98/1.61
% 0.98/1.61 useres = 1
% 0.98/1.61 useparamod = 1
% 0.98/1.61 useeqrefl = 1
% 0.98/1.61 useeqfact = 1
% 0.98/1.61 usefactor = 1
% 0.98/1.61 usesimpsplitting = 0
% 0.98/1.61 usesimpdemod = 5
% 0.98/1.61 usesimpres = 3
% 0.98/1.61
% 0.98/1.61 resimpinuse = 1000
% 0.98/1.61 resimpclauses = 20000
% 0.98/1.61 substype = eqrewr
% 0.98/1.61 backwardsubs = 1
% 0.98/1.61 selectoldest = 5
% 0.98/1.61
% 0.98/1.61 litorderings [0] = split
% 0.98/1.61 litorderings [1] = extend the termordering, first sorting on arguments
% 0.98/1.61
% 0.98/1.61 termordering = kbo
% 0.98/1.61
% 0.98/1.61 litapriori = 0
% 0.98/1.61 termapriori = 1
% 0.98/1.61 litaposteriori = 0
% 0.98/1.61 termaposteriori = 0
% 0.98/1.61 demodaposteriori = 0
% 0.98/1.61 ordereqreflfact = 0
% 0.98/1.61
% 0.98/1.61 litselect = negord
% 0.98/1.61
% 0.98/1.61 maxweight = 15
% 0.98/1.61 maxdepth = 30000
% 0.98/1.61 maxlength = 115
% 0.98/1.61 maxnrvars = 195
% 0.98/1.61 excuselevel = 1
% 0.98/1.61 increasemaxweight = 1
% 0.98/1.61
% 0.98/1.61 maxselected = 10000000
% 0.98/1.61 maxnrclauses = 10000000
% 0.98/1.61
% 0.98/1.61 showgenerated = 0
% 0.98/1.61 showkept = 0
% 0.98/1.61 showselected = 0
% 0.98/1.61 showdeleted = 0
% 0.98/1.61 showresimp = 1
% 0.98/1.61 showstatus = 2000
% 0.98/1.61
% 0.98/1.61 prologoutput = 0
% 0.98/1.61 nrgoals = 5000000
% 0.98/1.61 totalproof = 1
% 0.98/1.61
% 0.98/1.61 Symbols occurring in the translation:
% 0.98/1.61
% 0.98/1.61 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.98/1.61 . [1, 2] (w:1, o:193, a:1, s:1, b:0),
% 0.98/1.61 ! [4, 1] (w:0, o:113, a:1, s:1, b:0),
% 0.98/1.61 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.98/1.61 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.98/1.61 hAPP [38, 2] (w:1, o:217, a:1, s:1, b:0),
% 0.98/1.61 v_n [39, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.98/1.61 tc_Nat_Onat [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.98/1.61 c_Groups_Ozero__class_Ozero [41, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.98/1.61 v_na____ [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.98/1.61 v_qa____ [43, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.98/1.61 tc_Complex_Ocomplex [44, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.98/1.61 tc_Polynomial_Opoly [45, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.98/1.61 v_s____ [46, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.98/1.61 c_Polynomial_Odegree [47, 2] (w:1, o:219, a:1, s:1, b:0),
% 0.98/1.61 v_p [48, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.98/1.61 v_a____ [49, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.98/1.61 v_pa____ [50, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.98/1.61 c_Polynomial_Oorder [51, 3] (w:1, o:254, a:1, s:1, b:0),
% 0.98/1.61 c_Groups_Otimes__class_Otimes [52, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.98/1.61 c_Power_Opower__class_Opower [53, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus [54, 2] (w:1, o:221, a:1, s:1, b:0),
% 0.98/1.61
% 0.98/1.61 c_Groups_Oone__class_Oone [55, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.98/1.61 c_Polynomial_OpCons [56, 3] (w:1, o:255, a:1, s:1, b:0),
% 0.98/1.61 v_r____ [57, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.98/1.61 c_Rings_Odvd__class_Odvd [59, 3] (w:1, o:256, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Ocomm__semiring__1 [63, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.98/1.61 c_Orderings_Oord__class_Oless [64, 3] (w:1, o:252, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Olinordered__semidom [65, 1] (w:1, o:130, a:1, s:1, b:0)
% 0.98/1.61 ,
% 0.98/1.61 class_Groups_Ozero [67, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Oring__1 [72, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.98/1.61 c_Polynomial_Opoly [73, 2] (w:1, o:222, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Omonoid__mult [79, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Oab__group__add [80, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.98/1.61 hBOOL [86, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Oidom [92, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Oring__1__no__zero__divisors [93, 1] (w:1, o:139, a:1, s:
% 0.98/1.61 1, b:0),
% 0.98/1.61 class_Groups_Ocomm__monoid__mult [95, 1] (w:1, o:140, a:1, s:1, b:0)
% 0.98/1.61 ,
% 0.98/1.61 class_Rings_Ocomm__semiring__0 [97, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.98/1.61 class_Power_Opower [99, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Omult__zero [100, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Ono__zero__divisors [101, 1] (w:1, o:153, a:1, s:1, b:0)
% 0.98/1.61 ,
% 0.98/1.61 class_Rings_Ozero__neq__one [102, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Osemiring__0 [103, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.98/1.61 v_q [105, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.98/1.61 c_Nat_OSuc [106, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq [107, 3] (w:1, o:253, a:1, s:1, b:0
% 0.98/1.61 ),
% 0.98/1.61 class_Rings_Ocomm__ring__1 [111, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.98/1.61 class_Int_Oring__char__0 [115, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Ocomm__ring [119, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Olinordered__ring [120, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Olinordered__ring__strict [121, 1] (w:1, o:129, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Rings_Oordered__cancel__semiring [122, 1] (w:1, o:160, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Rings_Oordered__ring [123, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Oordered__semiring [125, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.98/1.61
% 0.98/1.61 class_Rings_Oordered__comm__semiring [126, 1] (w:1, o:163, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Rings_Olinordered__semiring__strict [128, 1] (w:1, o:146, a:1
% 0.98/1.61 , s:1, b:0),
% 0.98/1.61 class_Rings_Olinordered__semiring [129, 1] (w:1, o:147, a:1, s:1, b:0
% 0.98/1.61 ),
% 0.98/1.61 class_Rings_Olinordered__idom [130, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Oring__no__zero__divisors [136, 1] (w:1, o:155, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Rings_Oring [137, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Odvd [138, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Olinordered__comm__semiring__strict [139, 1] (w:1, o:149
% 0.98/1.61 , a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Oordered__ab__group__add [141, 1] (w:1, o:166, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Groups_Oab__semigroup__mult [143, 1] (w:1, o:167, a:1, s:1, b:0
% 0.98/1.61 ),
% 0.98/1.61 class_Groups_Oone [144, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Ogroup__add [145, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Olinordered__ab__group__add [146, 1] (w:1, o:134, a:1
% 0.98/1.61 , s:1, b:0),
% 0.98/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [147, 2] (w:1, o:
% 0.98/1.61 220, a:1, s:1, b:0),
% 0.98/1.61 class_Orderings_Opreorder [148, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.98/1.61 class_Orderings_Olinorder [149, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.98/1.61 class_Orderings_Oord [150, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.98/1.61 tc_fun [151, 2] (w:1, o:232, a:1, s:1, b:0),
% 0.98/1.61 class_Orderings_Oorder [152, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.98/1.61 tc_Int_Oint [153, 0] (w:1, o:95, a:1, s:1, b:0),
% 0.98/1.61 c_Power_Opower_Opower [154, 3] (w:1, o:257, a:1, s:1, b:0),
% 0.98/1.61 c_Polynomial_Opcompose [155, 3] (w:1, o:258, a:1, s:1, b:0),
% 0.98/1.61 c_Polynomial_Opos__poly [156, 2] (w:1, o:233, a:1, s:1, b:0),
% 0.98/1.61 class_RealVector_Oreal__normed__algebra [157, 1] (w:1, o:170, a:1, s:
% 1.80/2.14 1, b:0),
% 1.80/2.14 class_Lattices_Oboolean__algebra [161, 1] (w:1, o:172, a:1, s:1, b:0)
% 1.80/2.14 ,
% 1.80/2.14 c_Polynomial_Omonom [162, 3] (w:1, o:259, a:1, s:1, b:0),
% 1.80/2.14 class_Lattices_Oab__semigroup__idem__mult [163, 1] (w:1, o:171, a:1
% 1.80/2.14 , s:1, b:0),
% 1.80/2.14 class_Groups_Ouminus [165, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.80/2.14 c_Polynomial_Opoly__rec [167, 5] (w:1, o:323, a:1, s:1, b:0),
% 1.80/2.14 c_Polynomial_Osynthetic__div [168, 3] (w:1, o:260, a:1, s:1, b:0),
% 1.80/2.14 c_Polynomial_Ocoeff [169, 2] (w:1, o:218, a:1, s:1, b:0),
% 1.80/2.14 c_Groups_Ominus__class_Ominus [170, 3] (w:1, o:261, a:1, s:1, b:0),
% 1.80/2.14 class_Groups_Ominus [174, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.80/2.14 c_fequal [183, 2] (w:1, o:234, a:1, s:1, b:0),
% 1.80/2.14 c_If [184, 4] (w:1, o:306, a:1, s:1, b:0),
% 1.80/2.14 c_Groups_Oplus__class_Oplus [187, 3] (w:1, o:262, a:1, s:1, b:0),
% 1.80/2.14 class_Groups_Ocomm__monoid__add [189, 1] (w:1, o:175, a:1, s:1, b:0)
% 1.80/2.14 ,
% 1.80/2.14 class_Groups_Ocancel__semigroup__add [190, 1] (w:1, o:176, a:1, s:1
% 1.80/2.14 , b:0),
% 1.80/2.14 class_Groups_Ocancel__ab__semigroup__add [191, 1] (w:1, o:177, a:1
% 1.80/2.14 , s:1, b:0),
% 1.80/2.14 class_Groups_Oab__semigroup__add [192, 1] (w:1, o:178, a:1, s:1, b:0)
% 1.80/2.14 ,
% 1.80/2.14 class_Groups_Oordered__ab__semigroup__add__imp__le [193, 1] (w:1, o:
% 1.80/2.14 179, a:1, s:1, b:0),
% 1.80/2.14 class_Groups_Oordered__ab__semigroup__add [194, 1] (w:1, o:180, a:1
% 1.80/2.14 , s:1, b:0),
% 1.80/2.14 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.80/2.14 195, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.80/2.14 class_Rings_Osemiring [197, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.80/2.14 class_Rings_Ocomm__semiring [198, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.80/2.14 class_Groups_Omonoid__add [199, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.80/2.14 class_Groups_Oordered__cancel__ab__semigroup__add [200, 1] (w:1, o:
% 1.80/2.14 187, a:1, s:1, b:0),
% 1.80/2.14 class_Groups_Oordered__comm__monoid__add [201, 1] (w:1, o:188, a:1
% 1.80/2.14 , s:1, b:0),
% 1.80/2.14 class_Rings_Olinordered__semiring__1 [207, 1] (w:1, o:150, a:1, s:1
% 1.80/2.14 , b:0),
% 1.80/2.14 class_Rings_Olinordered__semiring__1__strict [208, 1] (w:1, o:151, a:
% 1.80/2.14 1, s:1, b:0),
% 1.80/2.14 class_Fields_Ofield [210, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.80/2.14 c_Polynomial_Opdivmod__rel [211, 5] (w:1, o:324, a:1, s:1, b:0),
% 1.80/2.14 c_Nat__Transfer_Otsub [212, 2] (w:1, o:235, a:1, s:1, b:0),
% 1.80/2.14 c_Divides_Odiv__class_Odiv [225, 3] (w:1, o:263, a:1, s:1, b:0),
% 1.80/2.14 class_Divides_Osemiring__div [226, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.80/2.14 class_Divides_Oring__div [227, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.80/2.14 c_SMT_Oz3div [231, 2] (w:1, o:236, a:1, s:1, b:0),
% 1.80/2.14 c_Groups_Osgn__class_Osgn [232, 2] (w:1, o:237, a:1, s:1, b:0),
% 1.80/2.14 class_RealVector_Oreal__normed__vector [233, 1] (w:1, o:182, a:1, s:1
% 1.80/2.14 , b:0),
% 1.80/2.14 class_RealVector_Oreal__normed__algebra__1 [234, 1] (w:1, o:183, a:1
% 1.80/2.14 , s:1, b:0),
% 1.80/2.14 class_RealVector_Oreal__normed__div__algebra [235, 1] (w:1, o:184, a:
% 1.80/2.14 1, s:1, b:0),
% 1.80/2.14 class_Groups_Osgn__if [236, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.80/2.14 c_Polynomial_Opoly__gcd [237, 3] (w:1, o:264, a:1, s:1, b:0),
% 1.80/2.14 c_Divides_Odiv__class_Omod [238, 3] (w:1, o:265, a:1, s:1, b:0),
% 1.80/2.14 class_Groups_Ocancel__comm__monoid__add [240, 1] (w:1, o:192, a:1, s:
% 1.80/2.14 1, b:0),
% 1.80/2.14 tc_HOL_Obool [242, 0] (w:1, o:94, a:1, s:1, b:0),
% 1.80/2.14 alpha1 [243, 3] (w:1, o:266, a:1, s:1, b:1),
% 1.80/2.14 alpha2 [244, 3] (w:1, o:270, a:1, s:1, b:1),
% 1.80/2.14 alpha3 [245, 2] (w:1, o:241, a:1, s:1, b:1),
% 1.80/2.14 alpha4 [246, 4] (w:1, o:310, a:1, s:1, b:1),
% 1.80/2.14 alpha5 [247, 4] (w:1, o:314, a:1, s:1, b:1),
% 1.80/2.14 alpha6 [248, 2] (w:1, o:242, a:1, s:1, b:1),
% 1.80/2.14 alpha7 [249, 2] (w:1, o:243, a:1, s:1, b:1),
% 1.80/2.14 alpha8 [250, 3] (w:1, o:271, a:1, s:1, b:1),
% 1.80/2.14 alpha9 [251, 3] (w:1, o:272, a:1, s:1, b:1),
% 1.80/2.14 alpha10 [252, 2] (w:1, o:244, a:1, s:1, b:1),
% 1.80/2.14 alpha11 [253, 2] (w:1, o:245, a:1, s:1, b:1),
% 1.80/2.14 alpha12 [254, 3] (w:1, o:267, a:1, s:1, b:1),
% 1.80/2.14 alpha13 [255, 3] (w:1, o:268, a:1, s:1, b:1),
% 1.80/2.14 alpha14 [256, 2] (w:1, o:246, a:1, s:1, b:1),
% 1.80/2.14 alpha15 [257, 2] (w:1, o:247, a:1, s:1, b:1),
% 1.80/2.14 alpha16 [258, 2] (w:1, o:248, a:1, s:1, b:1),
% 13.58/13.90 alpha17 [259, 2] (w:1, o:249, a:1, s:1, b:1),
% 13.58/13.90 alpha18 [260, 4] (w:1, o:315, a:1, s:1, b:1),
% 13.58/13.90 alpha19 [261, 3] (w:1, o:269, a:1, s:1, b:1),
% 13.58/13.90 alpha20 [262, 3] (w:1, o:273, a:1, s:1, b:1),
% 13.58/13.90 alpha21 [263, 4] (w:1, o:316, a:1, s:1, b:1),
% 13.58/13.90 alpha22 [264, 4] (w:1, o:317, a:1, s:1, b:1),
% 13.58/13.90 alpha23 [265, 3] (w:1, o:274, a:1, s:1, b:1),
% 13.58/13.90 alpha24 [266, 2] (w:1, o:238, a:1, s:1, b:1),
% 13.58/13.90 alpha25 [267, 2] (w:1, o:239, a:1, s:1, b:1),
% 13.58/13.90 alpha26 [268, 3] (w:1, o:275, a:1, s:1, b:1),
% 13.58/13.90 alpha27 [269, 3] (w:1, o:276, a:1, s:1, b:1),
% 13.58/13.90 alpha28 [270, 2] (w:1, o:240, a:1, s:1, b:1),
% 13.58/13.90 alpha29 [271, 3] (w:1, o:277, a:1, s:1, b:1),
% 13.58/13.90 alpha30 [272, 3] (w:1, o:278, a:1, s:1, b:1),
% 13.58/13.90 alpha31 [273, 3] (w:1, o:279, a:1, s:1, b:1),
% 13.58/13.90 alpha32 [274, 4] (w:1, o:307, a:1, s:1, b:1),
% 13.58/13.90 alpha33 [275, 4] (w:1, o:308, a:1, s:1, b:1),
% 13.58/13.90 alpha34 [276, 3] (w:1, o:280, a:1, s:1, b:1),
% 13.58/13.90 alpha35 [277, 2] (w:1, o:250, a:1, s:1, b:1),
% 13.58/13.90 alpha36 [278, 3] (w:1, o:281, a:1, s:1, b:1),
% 13.58/13.90 alpha37 [279, 3] (w:1, o:282, a:1, s:1, b:1),
% 13.58/13.90 alpha38 [280, 4] (w:1, o:309, a:1, s:1, b:1),
% 13.58/13.90 alpha39 [281, 3] (w:1, o:283, a:1, s:1, b:1),
% 13.58/13.90 alpha40 [282, 3] (w:1, o:284, a:1, s:1, b:1),
% 13.58/13.90 alpha41 [283, 4] (w:1, o:311, a:1, s:1, b:1),
% 13.58/13.90 alpha42 [284, 3] (w:1, o:285, a:1, s:1, b:1),
% 13.58/13.90 alpha43 [285, 3] (w:1, o:286, a:1, s:1, b:1),
% 13.58/13.90 alpha44 [286, 3] (w:1, o:287, a:1, s:1, b:1),
% 13.58/13.90 alpha45 [287, 4] (w:1, o:312, a:1, s:1, b:1),
% 13.58/13.90 alpha46 [288, 4] (w:1, o:313, a:1, s:1, b:1),
% 13.58/13.90 alpha47 [289, 3] (w:1, o:288, a:1, s:1, b:1),
% 13.58/13.90 alpha48 [290, 2] (w:1, o:251, a:1, s:1, b:1),
% 13.58/13.90 alpha49 [291, 3] (w:1, o:289, a:1, s:1, b:1),
% 13.58/13.90 alpha50 [292, 3] (w:1, o:290, a:1, s:1, b:1),
% 13.58/13.90 alpha51 [293, 4] (w:1, o:318, a:1, s:1, b:1),
% 13.58/13.90 alpha52 [294, 4] (w:1, o:319, a:1, s:1, b:1),
% 13.58/13.90 alpha53 [295, 4] (w:1, o:320, a:1, s:1, b:1),
% 13.58/13.90 skol1 [296, 2] (w:1, o:223, a:1, s:1, b:1),
% 13.58/13.90 skol2 [297, 0] (w:1, o:12, a:1, s:1, b:1),
% 13.58/13.90 skol3 [298, 0] (w:1, o:13, a:1, s:1, b:1),
% 13.58/13.90 skol4 [299, 2] (w:1, o:224, a:1, s:1, b:1),
% 13.58/13.90 skol5 [300, 1] (w:1, o:119, a:1, s:1, b:1),
% 13.58/13.90 skol6 [301, 2] (w:1, o:225, a:1, s:1, b:1),
% 13.58/13.90 skol7 [302, 3] (w:1, o:291, a:1, s:1, b:1),
% 13.58/13.90 skol8 [303, 3] (w:1, o:292, a:1, s:1, b:1),
% 13.58/13.90 skol9 [304, 3] (w:1, o:293, a:1, s:1, b:1),
% 13.58/13.90 skol10 [305, 3] (w:1, o:294, a:1, s:1, b:1),
% 13.58/13.90 skol11 [306, 2] (w:1, o:226, a:1, s:1, b:1),
% 13.58/13.90 skol12 [307, 2] (w:1, o:227, a:1, s:1, b:1),
% 13.58/13.90 skol13 [308, 3] (w:1, o:295, a:1, s:1, b:1),
% 13.58/13.90 skol14 [309, 3] (w:1, o:296, a:1, s:1, b:1),
% 13.58/13.90 skol15 [310, 2] (w:1, o:228, a:1, s:1, b:1),
% 13.58/13.90 skol16 [311, 3] (w:1, o:297, a:1, s:1, b:1),
% 13.58/13.90 skol17 [312, 3] (w:1, o:298, a:1, s:1, b:1),
% 13.58/13.90 skol18 [313, 3] (w:1, o:299, a:1, s:1, b:1),
% 13.58/13.90 skol19 [314, 3] (w:1, o:300, a:1, s:1, b:1),
% 13.58/13.90 skol20 [315, 3] (w:1, o:301, a:1, s:1, b:1),
% 13.58/13.90 skol21 [316, 4] (w:1, o:321, a:1, s:1, b:1),
% 13.58/13.90 skol22 [317, 3] (w:1, o:302, a:1, s:1, b:1),
% 13.58/13.90 skol23 [318, 2] (w:1, o:229, a:1, s:1, b:1),
% 13.58/13.90 skol24 [319, 2] (w:1, o:230, a:1, s:1, b:1),
% 13.58/13.90 skol25 [320, 2] (w:1, o:231, a:1, s:1, b:1),
% 13.58/13.90 skol26 [321, 4] (w:1, o:322, a:1, s:1, b:1),
% 13.58/13.90 skol27 [322, 3] (w:1, o:303, a:1, s:1, b:1),
% 13.58/13.90 skol28 [323, 3] (w:1, o:304, a:1, s:1, b:1),
% 13.58/13.90 skol29 [324, 3] (w:1, o:305, a:1, s:1, b:1).
% 13.58/13.90
% 13.58/13.90
% 13.58/13.90 Starting Search:
% 13.58/13.90
% 13.58/13.90 *** allocated 113905 integers for clauses
% 13.58/13.90 *** allocated 170857 integers for clauses
% 13.58/13.90 Resimplifying inuse:
% 13.58/13.90 Done
% 13.58/13.90
% 13.58/13.90
% 13.58/13.90 Intermediate Status:
% 13.58/13.90 Generated: 3016
% 13.58/13.90 Kept: 2006
% 13.58/13.90 Inuse: 61
% 13.58/13.90 Deleted: 0
% 13.58/13.90 Deletedinuse: 0
% 13.58/13.90
% 13.58/13.90 *** allocated 256285 integers for clauses
% 13.58/13.90 *** allocated 170857 integers for termspace/termends
% 13.58/13.90 Resimplifying inuse:
% 13.58/13.90 Done
% 13.58/13.90
% 13.58/13.90 *** allocated 384427 integers for clauses
% 13.58/13.90
% 13.58/13.90 Intermediate Status:
% 13.58/13.90 Generated: 12816
% 13.58/13.90 Kept: 4284
% 13.58/13.90 Inuse: 158
% 13.58/13.90 Deleted: 3
% 13.58/13.90 Deletedinuse: 0
% 13.58/13.90
% 13.58/13.90 Resimplifying inuse:
% 13.58/13.90 Done
% 13.58/13.90
% 13.58/13.90 *** allocated 256285 integers for termspace/termends
% 13.58/13.90 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16
% 55.71/56.16 Intermediate Status:
% 55.71/56.16 Generated: 20849
% 55.71/56.16 Kept: 6295
% 55.71/56.16 Inuse: 222
% 55.71/56.16 Deleted: 4
% 55.71/56.16 Deletedinuse: 0
% 55.71/56.16
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16 *** allocated 576640 integers for clauses
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16 *** allocated 384427 integers for termspace/termends
% 55.71/56.16
% 55.71/56.16 Intermediate Status:
% 55.71/56.16 Generated: 27941
% 55.71/56.16 Kept: 8847
% 55.71/56.16 Inuse: 301
% 55.71/56.16 Deleted: 5
% 55.71/56.16 Deletedinuse: 0
% 55.71/56.16
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16 *** allocated 864960 integers for clauses
% 55.71/56.16
% 55.71/56.16 Intermediate Status:
% 55.71/56.16 Generated: 35455
% 55.71/56.16 Kept: 10925
% 55.71/56.16 Inuse: 345
% 55.71/56.16 Deleted: 11
% 55.71/56.16 Deletedinuse: 5
% 55.71/56.16
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16
% 55.71/56.16 Intermediate Status:
% 55.71/56.16 Generated: 42145
% 55.71/56.16 Kept: 12943
% 55.71/56.16 Inuse: 367
% 55.71/56.16 Deleted: 12
% 55.71/56.16 Deletedinuse: 6
% 55.71/56.16
% 55.71/56.16 *** allocated 576640 integers for termspace/termends
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16
% 55.71/56.16 Intermediate Status:
% 55.71/56.16 Generated: 47997
% 55.71/56.16 Kept: 14953
% 55.71/56.16 Inuse: 409
% 55.71/56.16 Deleted: 14
% 55.71/56.16 Deletedinuse: 7
% 55.71/56.16
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16 *** allocated 1297440 integers for clauses
% 55.71/56.16
% 55.71/56.16 Intermediate Status:
% 55.71/56.16 Generated: 58568
% 55.71/56.16 Kept: 17215
% 55.71/56.16 Inuse: 428
% 55.71/56.16 Deleted: 15
% 55.71/56.16 Deletedinuse: 7
% 55.71/56.16
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16
% 55.71/56.16 Intermediate Status:
% 55.71/56.16 Generated: 64472
% 55.71/56.16 Kept: 19641
% 55.71/56.16 Inuse: 448
% 55.71/56.16 Deleted: 15
% 55.71/56.16 Deletedinuse: 7
% 55.71/56.16
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16 Resimplifying clauses:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16 *** allocated 864960 integers for termspace/termends
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16
% 55.71/56.16 Intermediate Status:
% 55.71/56.16 Generated: 71224
% 55.71/56.16 Kept: 21646
% 55.71/56.16 Inuse: 484
% 55.71/56.16 Deleted: 464
% 55.71/56.16 Deletedinuse: 11
% 55.71/56.16
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16
% 55.71/56.16 Intermediate Status:
% 55.71/56.16 Generated: 81965
% 55.71/56.16 Kept: 24171
% 55.71/56.16 Inuse: 515
% 55.71/56.16 Deleted: 466
% 55.71/56.16 Deletedinuse: 11
% 55.71/56.16
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16
% 55.71/56.16 Intermediate Status:
% 55.71/56.16 Generated: 90757
% 55.71/56.16 Kept: 26254
% 55.71/56.16 Inuse: 535
% 55.71/56.16 Deleted: 466
% 55.71/56.16 Deletedinuse: 11
% 55.71/56.16
% 55.71/56.16 *** allocated 1946160 integers for clauses
% 55.71/56.16 Resimplifying inuse:
% 55.71/56.16 Done
% 55.71/56.16
% 55.71/56.16 *** allocated 1297440 integers for termspace/termends
% 55.71/56.16
% 55.71/56.16 Intermediate Status:
% 55.71/56.16 Generated: 99693
% 55.83/56.16 Kept: 28903
% 55.83/56.16 Inuse: 560
% 55.83/56.16 Deleted: 466
% 55.83/56.16 Deletedinuse: 11
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16
% 55.83/56.16 Intermediate Status:
% 55.83/56.16 Generated: 109691
% 55.83/56.16 Kept: 31814
% 55.83/56.16 Inuse: 605
% 55.83/56.16 Deleted: 466
% 55.83/56.16 Deletedinuse: 11
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16
% 55.83/56.16 Intermediate Status:
% 55.83/56.16 Generated: 117338
% 55.83/56.16 Kept: 35262
% 55.83/56.16 Inuse: 624
% 55.83/56.16 Deleted: 467
% 55.83/56.16 Deletedinuse: 11
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16
% 55.83/56.16 Intermediate Status:
% 55.83/56.16 Generated: 129370
% 55.83/56.16 Kept: 38853
% 55.83/56.16 Inuse: 649
% 55.83/56.16 Deleted: 467
% 55.83/56.16 Deletedinuse: 11
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16 Resimplifying clauses:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16
% 55.83/56.16 Intermediate Status:
% 55.83/56.16 Generated: 139587
% 55.83/56.16 Kept: 40928
% 55.83/56.16 Inuse: 669
% 55.83/56.16 Deleted: 1587
% 55.83/56.16 Deletedinuse: 11
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16 *** allocated 2919240 integers for clauses
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16
% 55.83/56.16 Intermediate Status:
% 55.83/56.16 Generated: 150667
% 55.83/56.16 Kept: 42941
% 55.83/56.16 Inuse: 692
% 55.83/56.16 Deleted: 1587
% 55.83/56.16 Deletedinuse: 11
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16
% 55.83/56.16 Intermediate Status:
% 55.83/56.16 Generated: 158787
% 55.83/56.16 Kept: 45038
% 55.83/56.16 Inuse: 704
% 55.83/56.16 Deleted: 1587
% 55.83/56.16 Deletedinuse: 11
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16
% 55.83/56.16 Intermediate Status:
% 55.83/56.16 Generated: 167286
% 55.83/56.16 Kept: 47179
% 55.83/56.16 Inuse: 719
% 55.83/56.16 Deleted: 1587
% 55.83/56.16 Deletedinuse: 11
% 55.83/56.16
% 55.83/56.16 *** allocated 1946160 integers for termspace/termends
% 55.83/56.16
% 55.83/56.16 Intermediate Status:
% 55.83/56.16 Generated: 175369
% 55.83/56.16 Kept: 50941
% 55.83/56.16 Inuse: 739
% 55.83/56.16 Deleted: 1587
% 55.83/56.16 Deletedinuse: 11
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16
% 55.83/56.16 Intermediate Status:
% 55.83/56.16 Generated: 187559
% 55.83/56.16 Kept: 52942
% 55.83/56.16 Inuse: 773
% 55.83/56.16 Deleted: 1587
% 55.83/56.16 Deletedinuse: 11
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16
% 55.83/56.16 Intermediate Status:
% 55.83/56.16 Generated: 198321
% 55.83/56.16 Kept: 57493
% 55.83/56.16 Inuse: 804
% 55.83/56.16 Deleted: 1587
% 55.83/56.16 Deletedinuse: 11
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16 Resimplifying inuse:
% 55.83/56.16 Done
% 55.83/56.16
% 55.83/56.16
% 55.83/56.16 Intermediate Status:
% 55.83/56.16 Generated: 203640
% 55.83/56.16 Kept: 59499
% 55.83/56.16 Inuse: 821
% 55.83/56.16 Deleted: 1587
% 55.83/56.16 Deletedinuse: 11
% 55.83/56.16
% 55.83/56.16
% 55.83/56.16 Intermediate Status:
% 55.83/56.16 Generated: 209982
% 55.83/56.16 Kept: 62186
% 55.83/56.16 Inuse: 839
% 190.06/190.42 Deleted: 1587
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying clauses:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 *** allocated 4378860 integers for clauses
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 217221
% 190.06/190.42 Kept: 66014
% 190.06/190.42 Inuse: 849
% 190.06/190.42 Deleted: 1865
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 223870
% 190.06/190.42 Kept: 68067
% 190.06/190.42 Inuse: 894
% 190.06/190.42 Deleted: 1865
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 230099
% 190.06/190.42 Kept: 70193
% 190.06/190.42 Inuse: 951
% 190.06/190.42 Deleted: 1873
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 239535
% 190.06/190.42 Kept: 72408
% 190.06/190.42 Inuse: 974
% 190.06/190.42 Deleted: 1875
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 248231
% 190.06/190.42 Kept: 74480
% 190.06/190.42 Inuse: 994
% 190.06/190.42 Deleted: 1875
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 *** allocated 2919240 integers for termspace/termends
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 258622
% 190.06/190.42 Kept: 76922
% 190.06/190.42 Inuse: 1024
% 190.06/190.42 Deleted: 1875
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 266118
% 190.06/190.42 Kept: 79154
% 190.06/190.42 Inuse: 1049
% 190.06/190.42 Deleted: 1875
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 276042
% 190.06/190.42 Kept: 81254
% 190.06/190.42 Inuse: 1069
% 190.06/190.42 Deleted: 1875
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying clauses:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 284784
% 190.06/190.42 Kept: 83471
% 190.06/190.42 Inuse: 1094
% 190.06/190.42 Deleted: 2535
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 292794
% 190.06/190.42 Kept: 85490
% 190.06/190.42 Inuse: 1117
% 190.06/190.42 Deleted: 2535
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 305031
% 190.06/190.42 Kept: 88588
% 190.06/190.42 Inuse: 1144
% 190.06/190.42 Deleted: 2535
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 314154
% 190.06/190.42 Kept: 90904
% 190.06/190.42 Inuse: 1159
% 190.06/190.42 Deleted: 2535
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 321017
% 190.06/190.42 Kept: 93360
% 190.06/190.42 Inuse: 1174
% 190.06/190.42 Deleted: 2535
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 327486
% 190.06/190.42 Kept: 95976
% 190.06/190.42 Inuse: 1184
% 190.06/190.42 Deleted: 2535
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 338687
% 190.06/190.42 Kept: 98159
% 190.06/190.42 Inuse: 1234
% 190.06/190.42 Deleted: 2535
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 346199
% 190.06/190.42 Kept: 100210
% 190.06/190.42 Inuse: 1259
% 190.06/190.42 Deleted: 2535
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 *** allocated 6568290 integers for clauses
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 352767
% 190.06/190.42 Kept: 102233
% 190.06/190.42 Inuse: 1281
% 190.06/190.42 Deleted: 2535
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying clauses:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 364750
% 190.06/190.42 Kept: 104809
% 190.06/190.42 Inuse: 1289
% 190.06/190.42 Deleted: 3189
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 377641
% 190.06/190.42 Kept: 106814
% 190.06/190.42 Inuse: 1327
% 190.06/190.42 Deleted: 3189
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 *** allocated 4378860 integers for termspace/termends
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 385593
% 190.06/190.42 Kept: 109154
% 190.06/190.42 Inuse: 1334
% 190.06/190.42 Deleted: 3189
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 393257
% 190.06/190.42 Kept: 111283
% 190.06/190.42 Inuse: 1344
% 190.06/190.42 Deleted: 3189
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 409968
% 190.06/190.42 Kept: 113346
% 190.06/190.42 Inuse: 1354
% 190.06/190.42 Deleted: 3189
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 Resimplifying inuse:
% 190.06/190.42 Done
% 190.06/190.42
% 190.06/190.42
% 190.06/190.42 Intermediate Status:
% 190.06/190.42 Generated: 417761
% 190.06/190.42 Kept: 115368
% 190.06/190.42 Inuse: 1364
% 190.06/190.42 Deleted: 3189
% 190.06/190.42 Deletedinuse: 11
% 190.06/190.42
% 190.06/190.42 ResimplifCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------