TSTP Solution File: SWW277+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW277+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.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 300.03s 300.41s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW277+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sat Jun 4 16:58:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.97/1.50 *** allocated 10000 integers for termspace/termends
% 0.97/1.50 *** allocated 10000 integers for clauses
% 0.97/1.50 *** allocated 10000 integers for justifications
% 0.97/1.50 *** allocated 15000 integers for termspace/termends
% 0.97/1.50 *** allocated 22500 integers for termspace/termends
% 0.97/1.50 *** allocated 33750 integers for termspace/termends
% 0.97/1.50 Bliksem 1.12
% 0.97/1.50
% 0.97/1.50
% 0.97/1.50 Automatic Strategy Selection
% 0.97/1.50
% 0.97/1.50 *** allocated 50625 integers for termspace/termends
% 0.97/1.50 *** allocated 75937 integers for termspace/termends
% 0.97/1.50 *** allocated 113905 integers for termspace/termends
% 0.97/1.50
% 0.97/1.50 Clauses:
% 0.97/1.50
% 0.97/1.50 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.97/1.50 { v_x____ = v_a____ }.
% 0.97/1.50 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ) }.
% 0.97/1.50 { ! v_s____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ) }.
% 0.97/1.50 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.97/1.50 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.97/1.50 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ) ) ) ), v_s____ ) ) }.
% 0.97/1.50 { v_qa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.97/1.50 ( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.97/1.50 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.97/1.50 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ) ) ) ), v_r____ ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.50 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.50 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.97/1.50 ) }.
% 0.97/1.50 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.97/1.50 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.50 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.50 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.50 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.50 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.97/1.50 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.50 { v_qa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.97/1.50 ( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.97/1.50 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.97/1.50 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ) ) ) ), skol2 ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.50 { v_pa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.97/1.50 ( tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.50 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.97/1.50 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.97/1.50 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.97/1.50 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.97/1.50 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 0.97/1.50 , v_s____ ) }.
% 0.97/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.50 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.97/1.50 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.97/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.50 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.97/1.50 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.97/1.50 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.50 ( X, Y ) ) }.
% 0.97/1.50 { ! v_na____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.50 { ! c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.50 { ! v_pa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 0.97/1.50 }.
% 0.97/1.50 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.97/1.50 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.97/1.50 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ) ) ) ), v_qa____ ) ) }.
% 0.97/1.50 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.50 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.97/1.50 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.97/1.50 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.97/1.50 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.97/1.50 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 0.97/1.50 , v_pa____ ) ) }.
% 0.97/1.50 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_a____ ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.50 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.97/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_qa____ ), X ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.50 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), v_x____ ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.50 { ! c_Polynomial_Odegree( tc_Complex_Ocomplex, v_s____ ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.50 tc_Nat_Onat ) ) = Y }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 0.97/1.50 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.50 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.97/1.50 ), Z ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.50 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.97/1.50 ), Z ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.50 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 0.97/1.50 ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.50 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 0.97/1.50 ) ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 0.97/1.50 .
% 0.97/1.50 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.97/1.50 , Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.97/1.50 , Y ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.50 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.50 ) ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.50 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.97/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.97/1.50 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.97/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.97/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.97/1.50 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.97/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 0.97/1.50 ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.97/1.50 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.97/1.50 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.97/1.50 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.97/1.50 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.50 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.50 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.50 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.50 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.50 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.50 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.50 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.50 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.50 = Y }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.50 = Y }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.50 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.50 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.50 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.50 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.50 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.50 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.50 ( X, Y ) ) }.
% 0.97/1.50 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.97/1.50 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.50 ) ), Y ) }.
% 0.97/1.50 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_pa____ ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.97/1.50 ), v_qa____ ), v_na____ ) ) ) }.
% 0.97/1.50 { v_pa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.97/1.50 ( tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.50 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.97/1.50 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.97/1.50 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.97/1.50 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.97/1.50 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 0.97/1.50 , skol3 ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.50 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.97/1.50 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.97/1.50 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.97/1.50 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.97/1.50 ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____,
% 0.97/1.50 v_pa____ ) ) ) ), v_pa____ ) ) }.
% 0.97/1.50 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.50 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.50 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.50 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.50 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.50 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.50 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 0.97/1.50 ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.50 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.97/1.50 Y ) ) ) ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.50 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.97/1.50 Y ) ) ) ), Y ) ) }.
% 0.97/1.50 { ! c_Polynomial_Odegree( tc_Complex_Ocomplex, v_s____ ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ),
% 0.97/1.50 v_pa____ ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly
% 0.97/1.50 ( tc_Complex_Ocomplex ) ), v_qa____ ), v_na____ ) ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.50 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 0.97/1.50 ) ) }.
% 0.97/1.50 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.50 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.50 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.50 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.50 = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.50 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.50 { ! v_n = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.50 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) = v_n }.
% 0.97/1.50 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.97/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.50 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_pa____ ) = v_na____ }.
% 0.97/1.50 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.50 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.97/1.50 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.97/1.50 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.97/1.50 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.97/1.50 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.50 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.50 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.50 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.97/1.50 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.97/1.50 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.97/1.50 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.97/1.50 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.97/1.50 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.50 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.97/1.50 c_Polynomial_Odegree( X, Y ) }.
% 0.97/1.50 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.50 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.97/1.50 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.50 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.50 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.50 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.97/1.50 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.50 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.50 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.97/1.50 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.97/1.50 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.97/1.50 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.97/1.50 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.97/1.50 ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.97/1.50 ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.50 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.97/1.50 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.97/1.50 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.50 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.50 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.50 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.97/1.50 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.50 tc_Nat_Onat ) ) = Y }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.50 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.97/1.50 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.97/1.50 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons
% 0.97/1.50 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.97/1.50 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X, Z,
% 0.97/1.50 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ),
% 0.97/1.50 hAPP( c_Polynomial_Opoly( X, Y ), c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.50 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.97/1.50 ) ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.97/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 0.97/1.50 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.50 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.50 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.50 .
% 0.97/1.50 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.50 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.50 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Nat_Onat ) }.
% 0.97/1.50 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.50 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.50 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.50 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.97/1.50 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.50 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.50 ( X ) }.
% 0.97/1.50 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.50 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), c_Nat_OSuc(
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.97/1.50 tc_Complex_Ocomplex, v_s____ ), v_na____ ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), ! hAPP(
% 0.97/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, Z ), skol4( T, Z ) ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.97/1.50 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y
% 0.97/1.50 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ), Z ), X ) ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), hAPP(
% 0.97/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol4( Y, Z ) ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.97/1.50 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.50 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y
% 0.97/1.50 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.97/1.50 tc_Complex_Ocomplex ) ), Z ), X ) ) ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Oorder(
% 0.97/1.50 tc_Complex_Ocomplex, X, v_pa____ ), v_na____ ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.50 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.50 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.97/1.50 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.97/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.50 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.50 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.97/1.50 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.97/1.50 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.50 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.97/1.50 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.50 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.50 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.97/1.50 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.50 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.97/1.50 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.50 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.50 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ),
% 0.97/1.50 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.50 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Polynomial_Opoly( X ) ),
% 0.97/1.50 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.97/1.50 c_Polynomial_Odegree( X, Y ) ) }.
% 0.97/1.50 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 0.97/1.50 .
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.50 X ) ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.97/1.50 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.50 , X ) ) }.
% 0.97/1.50 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 0.97/1.50 , Y ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.50 ), Y = X }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , alpha1( X, Y ), Y = X }.
% 0.97/1.50 { ! alpha1( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.50 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.50 , X ) ) }.
% 0.97/1.50 { ! alpha1( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.50 { ! alpha1( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , alpha1( X, Y ) }.
% 0.97/1.50 { ! alpha2( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.50 { ! alpha2( X, Y ), ! Y = X }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , Y = X, alpha2( X, Y ) }.
% 0.97/1.50 { ! alpha2( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.50 { ! alpha2( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.50 tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , alpha2( X, Y ) }.
% 0.97/1.50 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.50 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.50 , X ) ) }.
% 0.97/1.50 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.50 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.50 ), Y ) ) }.
% 0.97/1.50 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.50 , X ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.50 ), X = Y }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.50 ), Y ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , Y = X }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.50 ), Y = X }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.50 , X ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.50 ), Y ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.50 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.97/1.50 ), Z ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.97/1.50 ), Z ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.50 ), Y = X }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.50 ), Y = X }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.50 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.50 ) }.
% 0.97/1.50 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.50 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.97/1.50 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.97/1.50 ), Z ) ) }.
% 0.97/1.50 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.50 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.97/1.50 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.97/1.50 Z ), Y ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.50 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.97/1.50 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.50 ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.50 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.97/1.50 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.97/1.50 ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , ! Y = X }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.50 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.97/1.50 ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.50 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.97/1.50 ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , ! Y = X }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , ! X = Y }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.97/1.50 ), Z ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.97/1.50 Z ), Y ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.50 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.50 ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.50 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.97/1.50 ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.50 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.97/1.50 ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.50 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.97/1.50 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.50 ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.50 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.97/1.50 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.97/1.50 ) ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.50 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.50 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.50 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.97/1.50 ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.97/1.50 .
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.97/1.50 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.50 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { alpha47( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.50 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.50 { alpha47( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.97/1.50 ( X, Y ), Z ) ) }.
% 0.97/1.50 { ! alpha47( X, Y, Z ), alpha50( X, Y, Z ), Z = Y }.
% 0.97/1.50 { ! alpha47( X, Y, Z ), alpha50( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.97/1.50 ) ) }.
% 0.97/1.50 { ! alpha50( X, Y, Z ), alpha47( X, Y, Z ) }.
% 0.97/1.50 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha47( X, Y, Z ) }.
% 0.97/1.50 { ! alpha50( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.97/1.50 }.
% 0.97/1.50 { ! alpha50( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.97/1.50 X, Y ), Z ) ), alpha50( X, Y, Z ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.50 X, Y, Z ) }.
% 0.97/1.50 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.50 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.97/1.50 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.97/1.50 ) }.
% 0.97/1.50 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Nat_Onat ), X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.50 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.97/1.50 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X
% 0.97/1.50 ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.50 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Nat_Onat ), X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.50 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.97/1.50 .
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.50 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.50 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.97/1.50 }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.50 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.50 X ) ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.97/1.50 .
% 0.97/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.97/1.50 .
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.97/1.50 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.50 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.97/1.50 .
% 0.97/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.50 ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.50 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.50 , c_Nat_OSuc( X ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.97/1.50 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.97/1.50 }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.97/1.50 c_Nat_OSuc( X ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.50 ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.97/1.50 ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.97/1.50 ) }.
% 0.97/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.50 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.50 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.50 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.50 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.50 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.50 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.50 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.50 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.50 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.50 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.97/1.50 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.50 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.50 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.50 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.50 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.50 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.50 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.50 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.50 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.50 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.50 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.50 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.50 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.50 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.97/1.50 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.97/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.50 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.50 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.50 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.50 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.51 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.97/1.51 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.51 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.97/1.51 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.51 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.51 ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha3( X, Y ) }.
% 0.97/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.51 { ! alpha3( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.51 c_Nat_OSuc( X ) ) }.
% 0.97/1.51 { ! alpha3( X, Y ), Y = c_Nat_OSuc( skol5( Z, Y ) ) }.
% 0.97/1.51 { ! alpha3( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol5( X, Y
% 0.97/1.51 ), X ) }.
% 0.97/1.51 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.51 ), alpha3( X, Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol6( X ) ) }.
% 0.97/1.51 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.51 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.51 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.51 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.51 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.51 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 Y ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.51 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.51 ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.51 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.51 ), X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.97/1.51 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.97/1.51 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.51 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.51 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.97/1.51 .
% 0.97/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.51 .
% 0.97/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.51 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.51 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.51 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha4( X, Y, Z, T ),
% 0.97/1.51 alpha19( X, Y, Z, T ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z, T ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.51 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.51 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha19( X, Y, Z, T ) }.
% 0.97/1.51 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.97/1.51 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.97/1.51 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha4( X, Y, Z, T ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha5( X, Y, Z, T ),
% 0.97/1.51 alpha20( X, Y, Z, T ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z, T ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.51 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha20( X, Y, Z, T ) }.
% 0.97/1.51 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.51 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.51 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha5( X, Y, Z, T ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.51 .
% 0.97/1.51 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( X ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( X ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( X ) ), alpha6( X, Y, Z ), alpha21( X, Y, Z ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha21( X, Y, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( X ) ) }.
% 0.97/1.51 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( X ), Y ), alpha21( X, Y, Z ) }.
% 0.97/1.51 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.51 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ), alpha6( X, Y, Z ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha7( X, Y
% 0.97/1.51 , Z ), alpha22( X, Y, Z ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha22( X, Y, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ), alpha22( X, Y, Z ) }.
% 0.97/1.51 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.51 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Y ), alpha7( X, Y, Z ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.51 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.51 .
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.97/1.51 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP
% 0.97/1.51 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.51 ( X ), T ), Z ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y
% 0.97/1.51 ) ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ), hBOOL( hAPP( hAPP
% 0.97/1.51 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.51 ( X ), Z ), U ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T
% 0.97/1.51 ) ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.51 X ), T ), Z ) ), Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.97/1.51 , U, Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), U ) ), Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.51 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 Y ), X ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.97/1.51 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.51 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 X ), Y ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.97/1.51 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.97/1.51 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.51 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.51 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 X ), Y ), Z = Y }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.97/1.51 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 0.97/1.51 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.97/1.51 { ! X = c_Nat_OSuc( X ) }.
% 0.97/1.51 { ! c_Nat_OSuc( X ) = X }.
% 0.97/1.51 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.51 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.97/1.51 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.97/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.51 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), Z ), Y ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.51 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.97/1.51 }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.51 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Nat_Onat ) ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.51 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.51 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.97/1.51 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.51 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), hBOOL( hAPP
% 0.97/1.51 ( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.97/1.51 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), !
% 0.97/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ),
% 0.97/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.97/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.97/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.51 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hBOOL(
% 0.97/1.51 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.51 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.51 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.97/1.51 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.51 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.97/1.51 .
% 0.97/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.97/1.51 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.51 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.51 .
% 0.97/1.51 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.97/1.51 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.97/1.51 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.51 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.97/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Nat_Onat ) }.
% 0.97/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Nat_Onat ) }.
% 0.97/1.51 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.51 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.51 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.51 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.51 , Y ), X ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.97/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.97/1.51 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.51 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.97/1.51 , Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.97/1.51 ), Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.51 tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.51 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.97/1.51 , Y ) ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.51 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.51 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), Y ) }.
% 0.97/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.51 ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.51 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.97/1.51 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.51 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.51 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.51 tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.51 tc_Nat_Onat ), Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.97/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.97/1.51 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.51 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.51 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.51 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.51 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.51 .
% 0.97/1.51 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.51 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.51 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.51 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 , Y ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.51 , Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.97/1.51 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.97/1.51 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.51 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.97/1.51 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.51 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.51 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.51 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.51 = Y }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.51 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( X ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Y ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 = Y }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.51 = Y }.
% 0.97/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.51 = Y }.
% 0.97/1.51 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.51 = Y }.
% 0.97/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.51 = Y }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.51 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.51 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Y ), Z ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.51 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Z ), Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.51 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.51 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Y ), Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.97/1.51 , Y ) }.
% 0.97/1.51 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.97/1.51 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.51 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.51 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 0.97/1.51 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.51 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.97/1.51 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.97/1.51 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.97/1.51 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.97/1.51 ) ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.51 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.51 hAPP( Y, U ) ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.51 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.97/1.51 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.51 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.51 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.51 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.51 hAPP( Y, U ) ) }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.51 ( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.51 ( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.51 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.51 hAPP( Y, U ) ) }.
% 0.97/1.51 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.97/1.51 ( Z, skol7( X, Y, Z ) ), hAPP( Y, skol7( X, Y, Z ) ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.51 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.51 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.51 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.51 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.51 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.51 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.51 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.51 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.51 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.51 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.51 , ! Y = Z }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.51 , ! Z = Y }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.51 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.51 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.51 , ! Z = Y }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.51 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.51 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.51 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.51 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.51 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.51 Y ), ! Z = Y }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.51 Z ), ! Z = Y }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.51 Y ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.51 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.97/1.51 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X
% 0.97/1.51 ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 0.97/1.51 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.51 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.51 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.51 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.51 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.51 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.51 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.51 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.51 ( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.51 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.51 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.51 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.51 , ! Z = Y }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.51 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.51 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.51 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.97/1.51 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha8
% 0.97/1.51 ( X, Y, Z ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.51 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! alpha8( X, Y, Z ),
% 0.97/1.51 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.97/1.51 { ! alpha8( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.97/1.51 ( X ) ) }.
% 0.97/1.51 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.51 alpha8( X, Y, Z ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.51 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.51 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.97/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.97/1.51 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.51 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.97/1.51 ( tc_Int_Oint ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.51 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.51 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.97/1.51 .
% 0.97/1.51 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.51 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.97/1.51 }.
% 0.97/1.51 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.51 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.97/1.51 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.51 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.51 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.97/1.51 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Int_Oint ), X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.51 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.97/1.51 .
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.51 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.51 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.51 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.97/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Int_Oint ) ) }.
% 0.97/1.51 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.51 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ), hBOOL( hAPP( hAPP
% 0.97/1.51 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.51 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ), hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Int_Oint ) ) }.
% 0.97/1.51 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.51 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.51 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.51 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.97/1.51 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.97/1.51 X, Z ), Y ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.97/1.51 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.97/1.51 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.97/1.51 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.97/1.51 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.97/1.51 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.97/1.51 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.97/1.51 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.51 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.51 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.51 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Y ), Z = Y }.
% 0.97/1.51 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Y ) }.
% 0.97/1.51 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.51 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.97/1.51 ) ) }.
% 0.97/1.51 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.97/1.51 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.51 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.97/1.51 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.97/1.51 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.97/1.51 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.97/1.51 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.97/1.51 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.97/1.51 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.51 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.51 }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.97/1.51 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.51 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 0.97/1.51 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 0.97/1.51 , Y ) }.
% 0.97/1.51 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.51 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.97/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.97/1.51 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Omono( tc_Nat_Onat, X
% 0.97/1.51 , c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), T ), Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.97/1.51 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.97/1.51 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.97/1.51 hAPP( Z, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.97/1.51 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.51 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.51 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.51 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.51 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.51 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.51 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.51 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.51 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.97/1.51 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.97/1.51 T ) ) ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.51 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.51 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.97/1.51 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.97/1.51 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol8( X
% 0.97/1.51 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol8( X, Y, Z ) ), Z = Y
% 0.97/1.51 }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.97/1.51 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.97/1.51 c_Polynomial_Ocoeff( X, Y ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.97/1.51 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.97/1.51 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.51 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.51 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.51 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.97/1.51 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Nat_Onat ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.51 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.51 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( X ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.51 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , Z, Y ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.51 X, Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.97/1.51 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.51 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.51 ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.97/1.51 ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 0.97/1.51 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 0.97/1.51 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.51 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ) ) = Z }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.51 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.97/1.51 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.51 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.51 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.97/1.51 ) ) }.
% 0.97/1.51 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.97/1.51 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.97/1.51 c_Polynomial_Odegree( X, Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL
% 0.97/1.51 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Y ),
% 0.97/1.51 Z ) ), Z = Y }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.97/1.51 ) ) = X }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.97/1.51 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.51 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.97/1.51 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.97/1.51 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.97/1.51 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.97/1.51 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.97/1.51 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.97/1.51 ) }.
% 0.97/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.51 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.51 ( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.97/1.51 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.51 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.97/1.51 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.97/1.51 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.97/1.51 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.97/1.51 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.97/1.51 ( X ) }.
% 0.97/1.51 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.97/1.51 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.97/1.51 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.51 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.51 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.51 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.51 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.97/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.97/1.51 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.97/1.51 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.51 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.97/1.51 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.97/1.51 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) ), ! hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 Z, Y ) ) = Y }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.51 Y ) ) = Y }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.97/1.51 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.97/1.51 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.51 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, Z, Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, Z, Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.51 , T ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.51 , T, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.51 , Y, T ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, Z, Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.51 , T, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, T, Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.51 , Y, Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.51 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.51 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.51 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.51 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.97/1.51 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.51 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.97/1.51 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, Y, T
% 0.97/1.51 ) ) ) }.
% 0.97/1.51 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 Y, T ), Z = Y }.
% 0.97/1.51 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 T, Y ), Z = Y }.
% 0.97/1.51 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 T, Y ), Z = Y }.
% 0.97/1.51 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 Y, Z ), T = Y }.
% 0.97/1.51 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 Y, Z ) }.
% 0.97/1.51 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 T, Y ), Z = Y }.
% 0.97/1.51 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 T, Y ) }.
% 0.97/1.51 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.97/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.97/1.51 ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.51 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.51 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.51 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.51 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.51 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.51 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.51 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.51 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.51 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.51 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.51 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.51 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.97/1.51 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.51 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.51 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.51 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.51 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.51 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.51 ), U = Z, T = Y }.
% 0.97/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.51 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.51 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.97/1.51 ) ), T ), Y ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.97/1.51 ) ), Z ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.51 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.51 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.51 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.51 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.51 ), ! U = T }.
% 0.97/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.51 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.51 ), ! Z = Y }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.51 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.51 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.51 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.51 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.51 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.51 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.97/1.51 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.51 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.51 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.51 .
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.51 .
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.51 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 Y, Z ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 Z, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ) ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.51 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.97/1.51 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.51 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.51 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.51 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.51 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.97/1.51 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.51 , Y, T ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.51 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.51 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.51 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.51 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.51 Z ) = Y }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.51 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Y ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 X ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.51 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( X, Z ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.51 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.51 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.51 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.51 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.51 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.51 Z ) ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.51 W ) ), U ), Y ) }.
% 0.97/1.51 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.51 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), Z ), U ), Y ) }.
% 0.97/1.51 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.51 Z ) ), U ), T ) = Y }.
% 0.97/1.51 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.51 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), Z ), U ), Y ) }.
% 0.97/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.51 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.51 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.51 X, Z, Y ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.51 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.97/1.51 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.51 , Y ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.51 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.97/1.51 X, Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.51 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.97/1.51 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.97/1.51 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.97/1.51 }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.51 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.97/1.51 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.97/1.51 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.51 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.97/1.51 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.97/1.51 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.51 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.97/1.51 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.97/1.51 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.51 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.97/1.51 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.97/1.51 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.97/1.51 .
% 0.97/1.51 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.97/1.51 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.51 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), Y ) }.
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.51 ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.51 ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.51 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.51 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.51 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.51 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.51 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.51 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.51 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.51 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.51 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.97/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.51 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.51 X, W, Z ) ), U ), T ), Y ) }.
% 0.97/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.51 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), Z ), U ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( X, Z, W ) ), U ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.51 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.97/1.51 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.97/1.51 hAPP( Z, skol9( U, W, Z ) ) ) }.
% 0.97/1.51 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.97/1.51 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.97/1.51 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, skol9( X, Y, Z ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 0.97/1.51 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.51 , T, c_Groups_Ozero__class_Ozero( X ) ) ) ), ! hBOOL( hAPP( Z, T ) ),
% 0.97/1.51 hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.97/1.51 skol28( X, Y, Z ) ) ) ) }.
% 0.97/1.51 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.97/1.51 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.97/1.51 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.97/1.51 .
% 0.97/1.51 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, U, T
% 0.97/1.51 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.97/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ), hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.51 , U, T ) ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, U, T
% 0.97/1.51 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.97/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ), hBOOL( hAPP(
% 0.97/1.51 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.51 , U, T ) ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.51 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.51 .
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.51 ( tc_Int_Oint ) ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.51 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.51 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.97/1.51 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.97/1.51 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.51 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.97/1.51 ), Y ) }.
% 0.97/1.51 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.51 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.97/1.51 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.97/1.51 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.97/1.51 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.97/1.51 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.97/1.51 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.51 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.51 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.97/1.51 }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.51 , alpha33( X, Y, Z, T ) }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha33( X, Y, Z, T ),
% 0.97/1.51 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.97/1.51 { ! alpha33( X, Y, Z, T ), alpha9( X, Z, T ) }.
% 0.97/1.51 { ! alpha33( X, Y, Z, T ), alpha23( X, Y, T ) }.
% 0.97/1.51 { ! alpha9( X, Z, T ), ! alpha23( X, Y, T ), alpha33( X, Y, Z, T ) }.
% 0.97/1.51 { ! alpha23( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), alpha34( X, Y, Z ) }.
% 0.97/1.51 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha23( X
% 0.97/1.51 , Y, Z ) }.
% 0.97/1.51 { ! alpha34( X, Y, Z ), alpha23( X, Y, Z ) }.
% 0.97/1.51 { ! alpha34( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.97/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha34( X
% 0.97/1.51 , Y, Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.97/1.51 ), c_Polynomial_Odegree( X, Z ) ), alpha34( X, Y, Z ) }.
% 0.97/1.51 { ! alpha9( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.51 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X, Y
% 0.97/1.51 , Z ) }.
% 0.97/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X
% 0.97/1.51 , Y, Z ) }.
% 0.97/1.51 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.51 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.97/1.51 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.97/1.51 , skol10( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Polynomial_Odegree( X, Y ), Z ) }.
% 0.97/1.51 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol10( X
% 0.97/1.51 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.97/1.51 Y ), Z ) }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.51 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.51 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.51 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.97/1.51 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.51 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.97/1.51 .
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.97/1.51 , X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.51 .
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.51 .
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.97/1.51 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.97/1.51 .
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.51 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.97/1.51 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.51 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol11( X, Y ) ) }.
% 0.97/1.51 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ) ) = X }.
% 0.97/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), X ) = X }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.51 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Int_Oint ), X ) = X }.
% 0.97/1.51 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Int_Oint ) ) = X }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.97/1.51 .
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.97/1.51 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.97/1.51 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.51 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.51 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.97/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.51 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha10( X, Y ),
% 0.97/1.51 alpha24( X, Y ) }.
% 0.97/1.51 { ! alpha10( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.51 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! alpha24( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.51 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! alpha24( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! alpha24( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ) ) }.
% 0.97/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha24( X, Y ) }.
% 0.97/1.51 { ! alpha10( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ) ) }.
% 0.97/1.51 { ! alpha10( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 0.97/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha11( X, Y ), alpha25( X
% 0.97/1.51 , Y ) }.
% 0.97/1.51 { ! alpha11( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.51 { ! alpha25( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.51 { ! alpha25( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! alpha25( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ) ) }.
% 0.97/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha25( X, Y ) }.
% 0.97/1.51 { ! alpha11( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ) ) }.
% 0.97/1.51 { ! alpha11( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.51 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol12( X, Y ) ) ) }.
% 0.97/1.51 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.97/1.51 .
% 0.97/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.97/1.51 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.97/1.51 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.97/1.51 = X }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Int_Oint ) ) ) }.
% 0.97/1.51 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Int_Oint ) ) ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.97/1.51 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.51 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.97/1.51 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.51 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.51 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.51 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) ), hBOOL( hAPP( hAPP(
% 0.97/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.51 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.97/1.51 , Z ), X ) ), T ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.51 tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) )
% 0.97/1.51 }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 0.97/1.51 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 0.97/1.51 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.97/1.51 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.51 , ! alpha12( X, Y, Z ) }.
% 0.97/1.51 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.51 , ! alpha26( X, Y, Z ) }.
% 0.97/1.51 { alpha12( X, Y, Z ), alpha26( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.51 { ! alpha26( X, Y, Z ), ! hBOOL( hAPP( Z, skol13( T, U, Z ) ) ) }.
% 0.97/1.51 { ! alpha26( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.51 skol13( X, Y, Z ) ) }.
% 0.97/1.51 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.97/1.51 ) ), alpha26( X, Y, Z ) }.
% 0.97/1.51 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.51 }.
% 0.97/1.51 { ! alpha12( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Nat_Onat ) ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12( X, Y, Z ) }.
% 0.97/1.51 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.51 , alpha13( X, Y, Z ) }.
% 0.97/1.51 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.51 , alpha27( X, Y, Z ) }.
% 0.97/1.51 { ! alpha13( X, Y, Z ), ! alpha27( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.51 { ! alpha27( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.51 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.51 { ! hBOOL( hAPP( Z, skol14( T, U, Z ) ) ), alpha27( X, Y, Z ) }.
% 0.97/1.51 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol14( X, Y, Z ) ),
% 0.97/1.51 alpha27( X, Y, Z ) }.
% 0.97/1.51 { ! alpha13( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.51 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha13( X, Y, Z ) }
% 0.97/1.51 .
% 0.97/1.51 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13
% 0.97/1.51 ( X, Y, Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.51 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.97/1.51 }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Int_Oint ) ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.97/1.51 }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Int_Oint ) ), X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.51 tc_Int_Oint ) ), X ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.97/1.51 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.51 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.97/1.51 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.97/1.51 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.97/1.51 ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.51 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 0.97/1.51 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.97/1.51 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.97/1.51 c_Polynomial_Odegree( X, Z ) ) }.
% 0.97/1.51 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.51 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.97/1.51 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.97/1.51 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.51 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.51 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.97/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.97/1.51 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.51 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.97/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.97/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.52 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.52 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.97/1.52 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.52 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.52 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.52 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.97/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.97/1.52 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.97/1.52 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.97/1.52 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.97/1.52 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.97/1.52 ( tc_Int_Oint ), Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.52 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.52 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.52 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.52 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.52 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.52 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.97/1.52 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.97/1.52 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.52 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.97/1.52 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.52 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.52 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.52 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.52 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.52 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.52 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.52 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.52 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.52 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.97/1.52 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.52 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.52 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.52 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.97/1.52 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.52 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.52 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.52 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.52 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.52 tc_Int_Oint, X, Y ) }.
% 0.97/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.52 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.97/1.52 ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol15( X, Y ) ) }.
% 0.97/1.52 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.97/1.52 ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.52 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.52 tc_Int_Oint, X, Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.97/1.52 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.97/1.52 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.97/1.52 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.52 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.97/1.52 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.52 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.97/1.52 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.52 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.97/1.52 ( X ) ) ) }.
% 0.97/1.52 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha14( X, Y ) }.
% 0.97/1.52 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.52 { ! alpha14( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.52 { ! alpha14( X, Y ), alpha28( X, Y ), alpha35( X, Y ) }.
% 0.97/1.52 { ! alpha28( X, Y ), alpha14( X, Y ) }.
% 0.97/1.52 { ! alpha35( X, Y ), alpha14( X, Y ) }.
% 0.97/1.52 { ! alpha35( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.52 { ! alpha35( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha35( X, Y ) }.
% 0.97/1.52 { ! alpha28( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.52 { ! alpha28( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha28( X, Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.97/1.52 , Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.97/1.52 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.52 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.97/1.52 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.52 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.52 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, X, Y ), X ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.97/1.52 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, Z, Y ), X ) }.
% 0.97/1.52 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.97/1.52 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.97/1.52 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.97/1.52 .
% 0.97/1.52 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.52 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.97/1.52 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.97/1.52 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.97/1.52 .
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.97/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.97/1.52 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.52 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.52 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 }.
% 0.97/1.52 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.52 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.52 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.52 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.52 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.97/1.52 }.
% 0.97/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.52 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.52 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.52 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.97/1.52 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.52 ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.52 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.52 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.52 .
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.52 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.52 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.52 .
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.52 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.97/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.52 .
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.52 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.97/1.52 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.97/1.52 .
% 0.97/1.52 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.52 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.52 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.97/1.52 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.52 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.97/1.52 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.52 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), c_Divides_Odiv__class_Odiv( X, Y
% 0.97/1.52 , Z ) ) = Y }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Odiv( X, Y
% 0.97/1.52 , Z ) ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.97/1.52 ), Z ) = Y }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.97/1.52 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.97/1.52 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.97/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.52 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.52 c_Power_Opower__class_Opower( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.97/1.52 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.52 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.52 c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ), hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.52 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.97/1.52 }.
% 0.97/1.52 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.97/1.52 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.52 { ! class_Divides_Oring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Odiv( X
% 0.97/1.52 , Y, c_Groups_Ouminus__class_Ouminus( X, Z ) ) =
% 0.97/1.52 c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.97/1.52 ) }.
% 0.97/1.52 { ! class_Divides_Oring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Odiv( X
% 0.97/1.52 , c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) =
% 0.97/1.52 c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.97/1.52 ) }.
% 0.97/1.52 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.97/1.52 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.52 ( tc_Int_Oint, Y ), X ) }.
% 0.97/1.52 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.52 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), c_Divides_Odiv__class_Odiv( X
% 0.97/1.52 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.97/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.97/1.52 ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.97/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.97/1.52 ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.97/1.52 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.97/1.52 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.97/1.52 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.97/1.52 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! c_Divides_Odiv__class_Odiv(
% 0.97/1.52 X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 0.97/1.52 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), !
% 0.97/1.52 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T, Z = hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.97/1.52 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), ! Z =
% 0.97/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.52 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.52 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.52 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.52 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.52 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.52 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.52 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.52 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.52 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.52 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.52 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.52 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.52 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.52 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.52 }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.52 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.52 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.52 .
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.52 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.52 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.52 }.
% 0.97/1.52 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.52 alpha15( X, Z ) }.
% 0.97/1.52 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.52 alpha29( X, Y, Z ) }.
% 0.97/1.52 { ! alpha15( X, Z ), ! alpha29( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.52 { ! alpha29( X, Y, Z ), alpha36( X, Y, Z ) }.
% 0.97/1.52 { ! alpha29( X, Y, Z ), alpha39( X, Y, Z ) }.
% 0.97/1.52 { ! alpha36( X, Y, Z ), ! alpha39( X, Y, Z ), alpha29( X, Y, Z ) }.
% 0.97/1.52 { ! alpha39( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha42( X, Y, Z ) }.
% 0.97/1.52 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha39( X, Y, Z ) }.
% 0.97/1.52 { ! alpha42( X, Y, Z ), alpha39( X, Y, Z ) }.
% 0.97/1.52 { ! alpha42( X, Y, Z ), ! alpha44( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.52 { ! hBOOL( hAPP( Z, skol16( T, U, Z ) ) ), alpha42( X, Y, Z ) }.
% 0.97/1.52 { alpha44( X, Y, skol16( X, Y, Z ) ), alpha42( X, Y, Z ) }.
% 0.97/1.52 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.52 skol17( X, T, U ) ) }.
% 0.97/1.52 { ! alpha44( X, Y, Z ), alpha46( X, Y, Z, skol17( X, Y, Z ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha46( X, Y, Z
% 0.97/1.52 , T ), alpha44( X, Y, Z ) }.
% 0.97/1.52 { ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.52 { ! alpha46( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.97/1.52 .
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha46( X,
% 0.97/1.52 Y, Z, T ) }.
% 0.97/1.52 { ! alpha36( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha40( X, Y, Z ) }.
% 0.97/1.52 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), X ), alpha36( X, Y, Z ) }.
% 0.97/1.52 { ! alpha40( X, Y, Z ), alpha36( X, Y, Z ) }.
% 0.97/1.52 { ! alpha40( X, Y, Z ), ! alpha43( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.52 { ! hBOOL( hAPP( Z, skol18( T, U, Z ) ) ), alpha40( X, Y, Z ) }.
% 0.97/1.52 { alpha43( X, Y, skol18( X, Y, Z ) ), alpha40( X, Y, Z ) }.
% 0.97/1.52 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol19( T, U, W ) ) }.
% 0.97/1.52 { ! alpha43( X, Y, Z ), alpha45( X, Y, Z, skol19( X, Y, Z ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha45( X, Y, Z, T )
% 0.97/1.52 , alpha43( X, Y, Z ) }.
% 0.97/1.52 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.97/1.52 ) }.
% 0.97/1.52 { ! alpha45( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.97/1.52 .
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha45( X,
% 0.97/1.52 Y, Z, T ) }.
% 0.97/1.52 { ! alpha15( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.52 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.52 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha15( X, Y ) }.
% 0.97/1.52 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha15
% 0.97/1.52 ( X, Y ) }.
% 0.97/1.52 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha48( X,
% 0.97/1.52 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, T, Z ) = Y }.
% 0.97/1.52 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha48( X,
% 0.97/1.52 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, T, Z ) = Y }.
% 0.97/1.52 { ! alpha48( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.52 { ! alpha48( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha48( X, Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.97/1.52 , alpha48( X, Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) }.
% 0.97/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.97/1.52 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.97/1.52 ( tc_Int_Oint, X, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }
% 0.97/1.52 .
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol20( Z, Y ) ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.97/1.52 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.97/1.52 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.52 tc_Int_Oint, skol20( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.52 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.97/1.52 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.52 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.97/1.52 , Z ), X ) ) ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.97/1.52 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.97/1.52 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.52 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.52 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.52 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.97/1.52 ( X ), Z, Y ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.97/1.52 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.52 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.97/1.52 ( X ), Z, Y ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.97/1.52 ( X ), T, Z ), Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.52 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.52 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.52 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.97/1.52 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.52 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.52 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.97/1.52 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.97/1.52 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.52 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.52 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.52 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.52 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.52 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.52 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.52 alpha16( X, Z ) }.
% 0.97/1.52 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.52 alpha30( X, Y, Z ) }.
% 0.97/1.52 { ! alpha16( X, Z ), ! alpha30( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.52 { ! alpha30( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.52 alpha37( X, Y, Z ) }.
% 0.97/1.52 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha30( X, Y, Z ) }.
% 0.97/1.52 { ! alpha37( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.97/1.52 { ! alpha37( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.97/1.52 ), alpha41( X, Y, Z, T ) }.
% 0.97/1.52 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol21( X, T, U ), X ),
% 0.97/1.52 alpha37( X, Y, Z ) }.
% 0.97/1.52 { ! alpha41( X, Y, Z, skol21( X, Y, Z ) ), alpha37( X, Y, Z ) }.
% 0.97/1.52 { ! alpha41( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.52 hBOOL( hAPP( Z, U ) ) }.
% 0.97/1.52 { ! hBOOL( hAPP( Z, skol22( U, W, Z, V0 ) ) ), alpha41( X, Y, Z, T ) }.
% 0.97/1.52 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol22( X, Y, Z, T ) )
% 0.97/1.52 , T ), alpha41( X, Y, Z, T ) }.
% 0.97/1.52 { ! alpha16( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.52 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.52 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha16( X, Y ) }.
% 0.97/1.52 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16
% 0.97/1.52 ( X, Y ) }.
% 0.97/1.52 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.52 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ) }.
% 0.97/1.52 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.97/1.52 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.52 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.52 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.97/1.52 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.97/1.52 tc_Int_Oint ) ) }.
% 0.97/1.52 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.52 alpha17( X, Z ), alpha31( X, Y, Z ) }.
% 0.97/1.52 { ! alpha17( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.52 { ! alpha31( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.52 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol23( X
% 0.97/1.52 , Y, T ) ), Y ) }.
% 0.97/1.52 { ! alpha31( X, Y, Z ), alpha38( X, Y, Z, skol23( X, Y, Z ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ), Y ), ! alpha38( X
% 0.97/1.52 , Y, Z, T ), alpha31( X, Y, Z ) }.
% 0.97/1.52 { ! alpha38( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 0.97/1.52 ( T ) ) ) }.
% 0.97/1.52 { ! alpha38( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 0.97/1.52 hBOOL( hAPP( Z, T ) ), alpha38( X, Y, Z, T ) }.
% 0.97/1.52 { ! alpha17( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.52 { ! alpha17( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Nat_Onat ) ) ) }.
% 0.97/1.52 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17( X, Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ),
% 0.97/1.52 ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ), Z
% 0.97/1.52 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.97/1.52 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.97/1.52 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 0.97/1.52 .
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.97/1.52 , Y ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.52 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.52 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol24( Z, Y ) ) ), !
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.97/1.52 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.97/1.52 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.97/1.52 tc_Int_Oint, skol24( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.52 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.97/1.52 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.97/1.52 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.97/1.52 ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.52 }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.97/1.52 .
% 0.97/1.52 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.97/1.52 .
% 0.97/1.52 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Y ) ) }
% 0.97/1.52 .
% 0.97/1.52 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Z ) ) }
% 0.97/1.52 .
% 0.97/1.52 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.97/1.52 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.52 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.97/1.52 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.52 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.97/1.52 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.97/1.52 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.52 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), T ) ), hBOOL(
% 0.97/1.52 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Y, T ) ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.52 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 0.97/1.52 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.97/1.52 , T ), Z ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.52 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 0.97/1.52 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.97/1.52 , T ), Y ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.52 ( tc_Polynomial_Opoly( X ) ), T ), Z ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ), hBOOL(
% 0.97/1.52 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.52 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha51( X, Y, Z, T ), ! Y =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.52 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.52 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha51( X, Y, Z, T ), ! hAPP(
% 0.97/1.52 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.97/1.52 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.97/1.52 .
% 0.97/1.52 { ! alpha51( X, Y, Z, T ), alpha52( X, Y, Z, T ), alpha49( X, Y, T ) }.
% 0.97/1.52 { ! alpha51( X, Y, Z, T ), alpha52( X, Y, Z, T ), ! hAPP(
% 0.97/1.52 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.52 { ! alpha52( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 0.97/1.52 { ! alpha49( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.97/1.52 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.52 alpha51( X, Y, Z, T ) }.
% 0.97/1.52 { ! alpha52( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), Z ), T ) ), alpha53( X, Y, Z, T ) }.
% 0.97/1.52 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 0.97/1.52 Z ), T ) ), alpha52( X, Y, Z, T ) }.
% 0.97/1.52 { ! alpha53( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 0.97/1.52 { ! alpha53( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), skol25( X, Y, U, W ) ), Y ) ) }.
% 0.97/1.52 { ! alpha53( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), skol25( X, Y, U, T ) ), T ) ) }.
% 0.97/1.52 { ! alpha53( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), skol25( X, Y, Z, T ) ), Z ) ) }.
% 0.97/1.52 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.97/1.52 , U ), Y ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.52 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), U ), Z ) ), alpha53
% 0.97/1.52 ( X, Y, Z, T ) }.
% 0.97/1.52 { ! alpha49( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! alpha49( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha49( X, Y, Z
% 0.97/1.52 ) }.
% 0.97/1.52 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.52 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol26( Z, Y
% 0.97/1.52 ), Y ) }.
% 0.97/1.52 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.52 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.52 skol26( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.97/1.52 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.52 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.97/1.52 , skol26( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.97/1.52 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.97/1.52 ) ), ! alpha18( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), alpha18( X, Y, skol27( X, Y, Z ), skol29( X, Y, Z )
% 0.97/1.52 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.97/1.52 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.52 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol27( X, Y, Z ) ), skol29
% 0.97/1.52 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.97/1.52 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.97/1.52 ) }.
% 0.97/1.52 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.97/1.52 { ! alpha18( X, Y, Z, T ), alpha32( X, Y, Z, T ) }.
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha32( X, Y, Z, T )
% 0.97/1.52 , alpha18( X, Y, Z, T ) }.
% 0.97/1.52 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.97/1.52 ) }.
% 0.97/1.52 { ! alpha32( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.97/1.52 .
% 0.97/1.52 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.97/1.52 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.52 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha32( X,
% 0.97/1.52 Y, Z, T ) }.
% 0.97/1.52 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.52 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.52 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.97/1.52 ( tc_fun( Y, X ) ) }.
% 0.97/1.52 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.97/1.52 ) ) }.
% 0.97/1.52 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.97/1.52 .
% 0.97/1.52 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.97/1.52 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.97/1.52 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.97/1.52 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.52 tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.97/1.52 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.97/1.52 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.97/1.52 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.97/1.52 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.97/1.52 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.97/1.52 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.97/1.52 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.97/1.52 { class_Power_Opower( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.97/1.52 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.97/1.52 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.97/1.52 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.52 tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.97/1.52 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.97/1.52 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.97/1.52 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.97/1.52 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.97/1.52 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.97/1.52 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.97/1.52 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.52 tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.97/1.52 { ! class_Rings_Oidom( X ),
% 0.97/1.52 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.52 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.97/1.52 ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.52 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.97/1.52 X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.52 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.97/1.52 ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.52 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.97/1.52 }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.52 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.52 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.52 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.52 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.52 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.52 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.52 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.52 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.52 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.52 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.52 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.97/1.52 ( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.97/1.52 ( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.97/1.52 ( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.97/1.52 }.
% 0.97/1.52 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.97/1.52 ) ) }.
% 0.97/1.52 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.97/1.52 .
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.97/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.52 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.97/1.52 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.97/1.52 { ! v_s____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.52 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.97/1.52 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.97/1.52 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.97/1.52 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.97/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.97/1.52 ) ) ), X ), v_thesis____ }.
% 0.97/1.52 { ! v_thesis____ }.
% 0.97/1.52
% 0.97/1.52 *** allocated 15000 integers for clauses
% 0.97/1.52 *** allocated 22500 integers for clauses
% 0.97/1.52 *** allocated 33750 integers for clauses
% 0.97/1.52 *** allocated 50625 integers for clauses
% 0.97/1.52 *** allocated 75937 integers for clauses
% 0.97/1.52 percentage equality = 0.262533, percentage horn = 0.900783
% 0.97/1.52 This is a problem with some equality
% 0.97/1.52
% 0.97/1.52
% 0.97/1.52
% 0.97/1.52 Options Used:
% 0.97/1.52
% 0.97/1.52 useres = 1
% 0.97/1.52 useparamod = 1
% 0.97/1.52 useeqrefl = 1
% 0.97/1.52 useeqfact = 1
% 0.97/1.52 usefactor = 1
% 0.97/1.52 usesimpsplitting = 0
% 0.97/1.52 usesimpdemod = 5
% 0.97/1.52 usesimpres = 3
% 0.97/1.52
% 0.97/1.52 resimpinuse = 1000
% 0.97/1.52 resimpclauses = 20000
% 0.97/1.52 substype = eqrewr
% 0.97/1.52 backwardsubs = 1
% 0.97/1.52 selectoldest = 5
% 0.97/1.52
% 0.97/1.52 litorderings [0] = split
% 0.97/1.52 litorderings [1] = extend the termordering, first sorting on arguments
% 0.97/1.52
% 0.97/1.52 termordering = kbo
% 0.97/1.52
% 0.97/1.52 litapriori = 0
% 0.97/1.52 termapriori = 1
% 0.97/1.52 litaposteriori = 0
% 0.97/1.52 termaposteriori = 0
% 0.97/1.52 demodaposteriori = 0
% 0.97/1.52 ordereqreflfact = 0
% 0.97/1.52
% 0.97/1.52 litselect = negord
% 0.97/1.52
% 0.97/1.52 maxweight = 15
% 0.97/1.52 maxdepth = 30000
% 0.97/1.52 maxlength = 115
% 0.97/1.52 maxnrvars = 195
% 0.97/1.52 excuselevel = 1
% 0.97/1.52 increasemaxweight = 1
% 0.97/1.52
% 0.97/1.52 maxselected = 10000000
% 0.97/1.52 maxnrclauses = 10000000
% 0.97/1.52
% 0.97/1.52 showgenerated = 0
% 0.97/1.52 showkept = 0
% 0.97/1.52 showselected = 0
% 0.97/1.52 showdeleted = 0
% 0.97/1.52 showresimp = 1
% 0.97/1.52 showstatus = 2000
% 0.97/1.52
% 0.97/1.52 prologoutput = 0
% 0.97/1.52 nrgoals = 5000000
% 0.97/1.52 totalproof = 1
% 0.97/1.52
% 0.97/1.52 Symbols occurring in the translation:
% 0.97/1.52
% 0.97/1.52 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.97/1.52 . [1, 2] (w:1, o:198, a:1, s:1, b:0),
% 0.97/1.52 ! [4, 1] (w:0, o:117, a:1, s:1, b:0),
% 0.97/1.52 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.52 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.52 hAPP [38, 2] (w:1, o:222, a:1, s:1, b:0),
% 0.97/1.52 v_x____ [39, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.97/1.52 v_a____ [40, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.97/1.52 v_qa____ [41, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.97/1.52 tc_Complex_Ocomplex [42, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.97/1.52 tc_Polynomial_Opoly [43, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.97/1.52 c_Groups_Ozero__class_Ozero [44, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.97/1.52 v_s____ [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.97/1.52 c_Rings_Odvd__class_Odvd [46, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.97/1.52 c_Groups_Ouminus__class_Ouminus [47, 2] (w:1, o:224, a:1, s:1, b:0),
% 0.97/1.52
% 0.97/1.52 c_Groups_Oone__class_Oone [48, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.97/1.52 c_Polynomial_OpCons [49, 3] (w:1, o:260, a:1, s:1, b:0),
% 0.97/1.52 hBOOL [50, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.97/1.52 c_Groups_Otimes__class_Otimes [51, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.97/1.52 v_r____ [52, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Ocomm__semiring__1 [54, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.97/1.52 class_Groups_Ozero [55, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Ocomm__ring__1 [59, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Oring__1__no__zero__divisors [61, 1] (w:1, o:135, a:1, s:
% 0.97/1.52 1, b:0),
% 0.97/1.52 class_Rings_Ocomm__semiring__0 [64, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.97/1.52 v_pa____ [66, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.97/1.52 c_Power_Opower__class_Opower [67, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.97/1.52 c_Polynomial_Oorder [68, 3] (w:1, o:259, a:1, s:1, b:0),
% 0.97/1.52 class_Groups_Oab__group__add [70, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Oring [73, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.97/1.52 v_na____ [74, 0] (w:1, o:43, a:1, s:1, b:0),
% 0.97/1.52 tc_Nat_Onat [75, 0] (w:1, o:44, a:1, s:1, b:0),
% 0.97/1.52 c_Polynomial_Opoly [76, 2] (w:1, o:225, a:1, s:1, b:0),
% 0.97/1.52 c_Polynomial_Odegree [77, 2] (w:1, o:227, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Odvd [80, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Oidom [86, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Ono__zero__divisors [92, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.97/1.52
% 0.97/1.52 class_Rings_Oring__no__zero__divisors [93, 1] (w:1, o:153, a:1, s:1
% 0.97/1.52 , b:0),
% 0.97/1.52 class_Rings_Omult__zero [94, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Ozero__neq__one [95, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.97/1.52 c_Nat_OSuc [97, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Oring__1 [99, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.97/1.52 class_Power_Opower [100, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Osemiring__0 [101, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.97/1.52 class_Groups_Omonoid__mult [102, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.97/1.52 class_Groups_Ocomm__monoid__mult [103, 1] (w:1, o:165, a:1, s:1, b:0)
% 0.97/1.52 ,
% 0.97/1.52 v_n [104, 0] (w:1, o:74, a:1, s:1, b:0),
% 0.97/1.52 v_p [105, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.97/1.52 v_q [106, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.97/1.52 class_Int_Oring__char__0 [107, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Ocomm__ring [109, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.97/1.52 c_Orderings_Oord__class_Oless [112, 3] (w:1, o:257, a:1, s:1, b:0),
% 0.97/1.52 c_Orderings_Oord__class_Oless__eq [116, 3] (w:1, o:258, a:1, s:1, b:0
% 0.97/1.52 ),
% 0.97/1.52 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [117, 2] (w:1, o:
% 0.97/1.52 223, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Olinordered__idom [124, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Olinordered__semidom [125, 1] (w:1, o:145, a:1, s:1, b:0)
% 0.97/1.52 ,
% 0.97/1.52 class_Rings_Olinordered__semiring__strict [128, 1] (w:1, o:146, a:1
% 0.97/1.52 , s:1, b:0),
% 0.97/1.52 class_Rings_Olinordered__semiring [129, 1] (w:1, o:147, a:1, s:1, b:0
% 0.97/1.52 ),
% 0.97/1.52 class_Rings_Olinordered__ring__strict [130, 1] (w:1, o:143, a:1, s:1
% 0.97/1.52 , b:0),
% 0.97/1.52 class_Rings_Olinordered__comm__semiring__strict [133, 1] (w:1, o:148
% 0.97/1.52 , a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Olinordered__ring [134, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Oordered__cancel__semiring [135, 1] (w:1, o:167, a:1, s:1
% 0.97/1.52 , b:0),
% 0.97/1.52 class_Rings_Oordered__ring [136, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.97/1.52 class_Rings_Oordered__semiring [137, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.97/1.52
% 0.97/1.52 class_Rings_Oordered__comm__semiring [138, 1] (w:1, o:170, a:1, s:1
% 0.97/1.52 , b:0),
% 0.97/1.52 tc_Int_Oint [144, 0] (w:1, o:97, a:1, s:1, b:0),
% 0.97/1.52 class_Groups_Oordered__ab__group__add [145, 1] (w:1, o:171, a:1, s:1
% 0.97/1.52 , b:0),
% 0.97/1.52 class_Groups_Olinordered__ab__group__add [146, 1] (w:1, o:163, a:1
% 0.97/1.52 , s:1, b:0),
% 0.97/1.52 class_Groups_Oab__semigroup__mult [147, 1] (w:1, o:172, a:1, s:1, b:0
% 0.97/1.52 ),
% 0.97/1.52 class_Groups_Oone [148, 1] (w:1, o:173, a:1, s:1, b:0),
% 0.97/1.52 class_Groups_Ogroup__add [149, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.97/1.52 class_Orderings_Opreorder [150, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.97/1.52 c_Power_Opower_Opower [151, 3] (w:1, o:261, a:1, s:1, b:0),
% 0.97/1.52 c_Polynomial_Opcompose [152, 3] (w:1, o:262, a:1, s:1, b:0),
% 0.97/1.52 class_Orderings_Olinorder [155, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.97/1.52 class_Orderings_Oord [156, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.97/1.52 tc_fun [157, 2] (w:1, o:237, a:1, s:1, b:0),
% 0.97/1.52 class_Orderings_Oorder [158, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.97/1.52 c_Polynomial_Opos__poly [159, 2] (w:1, o:238, a:1, s:1, b:0),
% 0.97/1.52 class_RealVector_Oreal__normed__algebra [160, 1] (w:1, o:175, a:1, s:
% 0.97/1.52 1, b:0),
% 0.97/1.52 class_Lattices_Oboolean__algebra [170, 1] (w:1, o:177, a:1, s:1, b:0)
% 0.97/1.52 ,
% 0.97/1.52 c_Polynomial_Omonom [171, 3] (w:1, o:263, a:1, s:1, b:0),
% 0.97/1.52 c_Polynomial_Opoly__rec [172, 5] (w:1, o:328, a:1, s:1, b:0),
% 0.97/1.52 class_Lattices_Oab__semigroup__idem__mult [173, 1] (w:1, o:176, a:1
% 0.97/1.52 , s:1, b:0),
% 0.97/1.52 class_Groups_Ouminus [175, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.44/1.81 c_fequal [176, 2] (w:1, o:239, a:1, s:1, b:0),
% 1.44/1.81 c_If [177, 4] (w:1, o:310, a:1, s:1, b:0),
% 1.44/1.81 c_Polynomial_Osynthetic__div [178, 3] (w:1, o:264, a:1, s:1, b:0),
% 1.44/1.81 c_Polynomial_Ocoeff [179, 2] (w:1, o:226, a:1, s:1, b:0),
% 1.44/1.81 c_Groups_Ominus__class_Ominus [180, 3] (w:1, o:265, a:1, s:1, b:0),
% 1.44/1.81 c_Orderings_Oorder_Omono [181, 4] (w:1, o:311, a:1, s:1, b:0),
% 1.44/1.81 class_Groups_Ominus [183, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.44/1.81 c_Groups_Oplus__class_Oplus [188, 3] (w:1, o:266, a:1, s:1, b:0),
% 1.44/1.81 class_Groups_Ocomm__monoid__add [189, 1] (w:1, o:180, a:1, s:1, b:0)
% 1.44/1.81 ,
% 1.44/1.81 class_Groups_Oordered__ab__semigroup__add__imp__le [190, 1] (w:1, o:
% 1.44/1.81 181, a:1, s:1, b:0),
% 1.44/1.81 class_Groups_Oordered__cancel__ab__semigroup__add [191, 1] (w:1, o:
% 1.44/1.81 182, a:1, s:1, b:0),
% 1.44/1.81 class_Groups_Ocancel__semigroup__add [192, 1] (w:1, o:183, a:1, s:1
% 1.44/1.81 , b:0),
% 1.44/1.81 class_Groups_Ocancel__ab__semigroup__add [193, 1] (w:1, o:184, a:1
% 1.44/1.81 , s:1, b:0),
% 1.44/1.81 class_Groups_Oab__semigroup__add [194, 1] (w:1, o:185, a:1, s:1, b:0)
% 1.44/1.81 ,
% 1.44/1.81 class_Groups_Oordered__ab__semigroup__add [195, 1] (w:1, o:186, a:1
% 1.44/1.81 , s:1, b:0),
% 1.44/1.81 class_Groups_Omonoid__add [196, 1] (w:1, o:187, a:1, s:1, b:0),
% 1.44/1.81 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.44/1.81 197, 1] (w:1, o:192, a:1, s:1, b:0),
% 1.44/1.81 class_Rings_Osemiring [199, 1] (w:1, o:188, a:1, s:1, b:0),
% 1.44/1.81 class_Rings_Ocomm__semiring [200, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.44/1.81 class_Groups_Oordered__comm__monoid__add [201, 1] (w:1, o:193, a:1
% 1.44/1.81 , s:1, b:0),
% 1.44/1.81 class_Rings_Olinordered__semiring__1 [208, 1] (w:1, o:149, a:1, s:1
% 1.44/1.81 , b:0),
% 1.44/1.81 class_Rings_Olinordered__semiring__1__strict [209, 1] (w:1, o:150, a:
% 1.44/1.81 1, s:1, b:0),
% 1.44/1.81 class_Fields_Ofield [211, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.44/1.81 c_Polynomial_Opdivmod__rel [212, 5] (w:1, o:329, a:1, s:1, b:0),
% 1.44/1.81 c_Nat__Transfer_Otsub [226, 2] (w:1, o:240, a:1, s:1, b:0),
% 1.44/1.81 c_Divides_Odiv__class_Odiv [227, 3] (w:1, o:267, a:1, s:1, b:0),
% 1.44/1.81 c_Groups_Osgn__class_Osgn [228, 2] (w:1, o:241, a:1, s:1, b:0),
% 1.44/1.81 class_RealVector_Oreal__normed__vector [229, 1] (w:1, o:189, a:1, s:1
% 1.44/1.81 , b:0),
% 1.44/1.81 class_RealVector_Oreal__normed__algebra__1 [230, 1] (w:1, o:190, a:1
% 1.44/1.81 , s:1, b:0),
% 1.44/1.81 class_Groups_Osgn__if [231, 1] (w:1, o:194, a:1, s:1, b:0),
% 1.44/1.81 class_RealVector_Oreal__normed__div__algebra [232, 1] (w:1, o:191, a:
% 1.44/1.81 1, s:1, b:0),
% 1.44/1.81 class_Divides_Osemiring__div [233, 1] (w:1, o:196, a:1, s:1, b:0),
% 1.44/1.81 class_Divides_Oring__div [234, 1] (w:1, o:195, a:1, s:1, b:0),
% 1.44/1.81 c_SMT_Oz3div [238, 2] (w:1, o:242, a:1, s:1, b:0),
% 1.44/1.81 c_Polynomial_Opoly__gcd [239, 3] (w:1, o:268, a:1, s:1, b:0),
% 1.44/1.81 c_Divides_Odiv__class_Omod [240, 3] (w:1, o:269, a:1, s:1, b:0),
% 1.44/1.81 class_Groups_Ocancel__comm__monoid__add [242, 1] (w:1, o:197, a:1, s:
% 1.44/1.81 1, b:0),
% 1.44/1.81 tc_HOL_Obool [244, 0] (w:1, o:96, a:1, s:1, b:0),
% 1.44/1.81 v_thesis____ [247, 0] (w:1, o:116, a:1, s:1, b:0),
% 1.44/1.81 alpha1 [248, 2] (w:1, o:243, a:1, s:1, b:1),
% 1.44/1.81 alpha2 [249, 2] (w:1, o:250, a:1, s:1, b:1),
% 1.44/1.81 alpha3 [250, 2] (w:1, o:254, a:1, s:1, b:1),
% 1.44/1.81 alpha4 [251, 4] (w:1, o:315, a:1, s:1, b:1),
% 1.44/1.81 alpha5 [252, 4] (w:1, o:319, a:1, s:1, b:1),
% 1.44/1.81 alpha6 [253, 3] (w:1, o:271, a:1, s:1, b:1),
% 1.44/1.81 alpha7 [254, 3] (w:1, o:272, a:1, s:1, b:1),
% 1.44/1.81 alpha8 [255, 3] (w:1, o:273, a:1, s:1, b:1),
% 1.44/1.81 alpha9 [256, 3] (w:1, o:274, a:1, s:1, b:1),
% 1.44/1.81 alpha10 [257, 2] (w:1, o:244, a:1, s:1, b:1),
% 1.44/1.81 alpha11 [258, 2] (w:1, o:245, a:1, s:1, b:1),
% 1.44/1.81 alpha12 [259, 3] (w:1, o:275, a:1, s:1, b:1),
% 1.44/1.81 alpha13 [260, 3] (w:1, o:276, a:1, s:1, b:1),
% 1.44/1.81 alpha14 [261, 2] (w:1, o:246, a:1, s:1, b:1),
% 1.44/1.81 alpha15 [262, 2] (w:1, o:247, a:1, s:1, b:1),
% 1.44/1.81 alpha16 [263, 2] (w:1, o:248, a:1, s:1, b:1),
% 1.44/1.81 alpha17 [264, 2] (w:1, o:249, a:1, s:1, b:1),
% 1.44/1.81 alpha18 [265, 4] (w:1, o:320, a:1, s:1, b:1),
% 1.44/1.81 alpha19 [266, 4] (w:1, o:321, a:1, s:1, b:1),
% 1.44/1.81 alpha20 [267, 4] (w:1, o:322, a:1, s:1, b:1),
% 1.44/1.81 alpha21 [268, 3] (w:1, o:277, a:1, s:1, b:1),
% 14.09/14.44 alpha22 [269, 3] (w:1, o:278, a:1, s:1, b:1),
% 14.09/14.44 alpha23 [270, 3] (w:1, o:279, a:1, s:1, b:1),
% 14.09/14.44 alpha24 [271, 2] (w:1, o:251, a:1, s:1, b:1),
% 14.09/14.44 alpha25 [272, 2] (w:1, o:252, a:1, s:1, b:1),
% 14.09/14.44 alpha26 [273, 3] (w:1, o:280, a:1, s:1, b:1),
% 14.09/14.44 alpha27 [274, 3] (w:1, o:281, a:1, s:1, b:1),
% 14.09/14.44 alpha28 [275, 2] (w:1, o:253, a:1, s:1, b:1),
% 14.09/14.44 alpha29 [276, 3] (w:1, o:282, a:1, s:1, b:1),
% 14.09/14.44 alpha30 [277, 3] (w:1, o:283, a:1, s:1, b:1),
% 14.09/14.44 alpha31 [278, 3] (w:1, o:284, a:1, s:1, b:1),
% 14.09/14.44 alpha32 [279, 4] (w:1, o:312, a:1, s:1, b:1),
% 14.09/14.44 alpha33 [280, 4] (w:1, o:313, a:1, s:1, b:1),
% 14.09/14.44 alpha34 [281, 3] (w:1, o:285, a:1, s:1, b:1),
% 14.09/14.44 alpha35 [282, 2] (w:1, o:255, a:1, s:1, b:1),
% 14.09/14.44 alpha36 [283, 3] (w:1, o:286, a:1, s:1, b:1),
% 14.09/14.44 alpha37 [284, 3] (w:1, o:287, a:1, s:1, b:1),
% 14.09/14.44 alpha38 [285, 4] (w:1, o:314, a:1, s:1, b:1),
% 14.09/14.44 alpha39 [286, 3] (w:1, o:288, a:1, s:1, b:1),
% 14.09/14.44 alpha40 [287, 3] (w:1, o:289, a:1, s:1, b:1),
% 14.09/14.44 alpha41 [288, 4] (w:1, o:316, a:1, s:1, b:1),
% 14.09/14.44 alpha42 [289, 3] (w:1, o:290, a:1, s:1, b:1),
% 14.09/14.44 alpha43 [290, 3] (w:1, o:291, a:1, s:1, b:1),
% 14.09/14.44 alpha44 [291, 3] (w:1, o:292, a:1, s:1, b:1),
% 14.09/14.44 alpha45 [292, 4] (w:1, o:317, a:1, s:1, b:1),
% 14.09/14.44 alpha46 [293, 4] (w:1, o:318, a:1, s:1, b:1),
% 14.09/14.44 alpha47 [294, 3] (w:1, o:293, a:1, s:1, b:1),
% 14.09/14.44 alpha48 [295, 2] (w:1, o:256, a:1, s:1, b:1),
% 14.09/14.44 alpha49 [296, 3] (w:1, o:294, a:1, s:1, b:1),
% 14.09/14.44 alpha50 [297, 3] (w:1, o:270, a:1, s:1, b:1),
% 14.09/14.44 alpha51 [298, 4] (w:1, o:323, a:1, s:1, b:1),
% 14.09/14.44 alpha52 [299, 4] (w:1, o:324, a:1, s:1, b:1),
% 14.09/14.44 alpha53 [300, 4] (w:1, o:325, a:1, s:1, b:1),
% 14.09/14.44 skol1 [301, 2] (w:1, o:228, a:1, s:1, b:1),
% 14.09/14.44 skol2 [302, 0] (w:1, o:16, a:1, s:1, b:1),
% 14.09/14.44 skol3 [303, 0] (w:1, o:17, a:1, s:1, b:1),
% 14.09/14.44 skol4 [304, 2] (w:1, o:229, a:1, s:1, b:1),
% 14.09/14.44 skol5 [305, 2] (w:1, o:230, a:1, s:1, b:1),
% 14.09/14.44 skol6 [306, 1] (w:1, o:122, a:1, s:1, b:1),
% 14.09/14.44 skol7 [307, 3] (w:1, o:295, a:1, s:1, b:1),
% 14.09/14.44 skol8 [308, 3] (w:1, o:296, a:1, s:1, b:1),
% 14.09/14.44 skol9 [309, 3] (w:1, o:297, a:1, s:1, b:1),
% 14.09/14.44 skol10 [310, 3] (w:1, o:298, a:1, s:1, b:1),
% 14.09/14.44 skol11 [311, 2] (w:1, o:231, a:1, s:1, b:1),
% 14.09/14.44 skol12 [312, 2] (w:1, o:232, a:1, s:1, b:1),
% 14.09/14.44 skol13 [313, 3] (w:1, o:299, a:1, s:1, b:1),
% 14.09/14.44 skol14 [314, 3] (w:1, o:300, a:1, s:1, b:1),
% 14.09/14.44 skol15 [315, 2] (w:1, o:233, a:1, s:1, b:1),
% 14.09/14.44 skol16 [316, 3] (w:1, o:301, a:1, s:1, b:1),
% 14.09/14.44 skol17 [317, 3] (w:1, o:302, a:1, s:1, b:1),
% 14.09/14.44 skol18 [318, 3] (w:1, o:303, a:1, s:1, b:1),
% 14.09/14.44 skol19 [319, 3] (w:1, o:304, a:1, s:1, b:1),
% 14.09/14.44 skol20 [320, 2] (w:1, o:234, a:1, s:1, b:1),
% 14.09/14.44 skol21 [321, 3] (w:1, o:305, a:1, s:1, b:1),
% 14.09/14.44 skol22 [322, 4] (w:1, o:326, a:1, s:1, b:1),
% 14.09/14.44 skol23 [323, 3] (w:1, o:306, a:1, s:1, b:1),
% 14.09/14.44 skol24 [324, 2] (w:1, o:235, a:1, s:1, b:1),
% 14.09/14.44 skol25 [325, 4] (w:1, o:327, a:1, s:1, b:1),
% 14.09/14.44 skol26 [326, 2] (w:1, o:236, a:1, s:1, b:1),
% 14.09/14.44 skol27 [327, 3] (w:1, o:307, a:1, s:1, b:1),
% 14.09/14.44 skol28 [328, 3] (w:1, o:308, a:1, s:1, b:1),
% 14.09/14.44 skol29 [329, 3] (w:1, o:309, a:1, s:1, b:1).
% 14.09/14.44
% 14.09/14.44
% 14.09/14.44 Starting Search:
% 14.09/14.44
% 14.09/14.44 *** allocated 113905 integers for clauses
% 14.09/14.44 *** allocated 170857 integers for clauses
% 14.09/14.44 Resimplifying inuse:
% 14.09/14.44 Done
% 14.09/14.44
% 14.09/14.44
% 14.09/14.44 Intermediate Status:
% 14.09/14.44 Generated: 3101
% 14.09/14.44 Kept: 2041
% 14.09/14.44 Inuse: 50
% 14.09/14.44 Deleted: 1
% 14.09/14.44 Deletedinuse: 0
% 14.09/14.44
% 14.09/14.44 *** allocated 256285 integers for clauses
% 14.09/14.44 *** allocated 170857 integers for termspace/termends
% 14.09/14.44 Resimplifying inuse:
% 14.09/14.44 Done
% 14.09/14.44
% 14.09/14.44 Resimplifying inuse:
% 14.09/14.44 Done
% 14.09/14.44
% 14.09/14.44 *** allocated 384427 integers for clauses
% 14.09/14.44
% 14.09/14.44 Intermediate Status:
% 14.09/14.44 Generated: 7172
% 14.09/14.44 Kept: 4131
% 14.09/14.44 Inuse: 200
% 14.09/14.44 Deleted: 8
% 14.09/14.44 Deletedinuse: 2
% 14.09/14.44
% 14.09/14.44 *** allocated 256285 integers for termspace/termends
% 14.09/14.44 Resimplifying inuse:
% 14.09/14.44 Done
% 14.09/14.44
% 14.09/14.44 Resimplifying inuse:
% 14.09/14.44 Done
% 14.09/14.44
% 14.09/14.44
% 14.09/14.44 Intermediate Status:
% 14.09/14.44 Generated: 11611
% 14.09/14.44 Kept: 6413
% 14.09/14.44 Inuse: 274
% 14.09/14.44 Deleted: 9
% 14.09/14.44 Deletedinuse: 2
% 14.09/14.44
% 14.09/14.44 *** allocated 576640 integers for clauses
% 14.09/14.44 Resimplifying inuse:
% 14.09/14.44 Done
% 14.09/14.44
% 14.09/14.44 *** allocated 384427 integers for termspace/termends
% 14.09/14.44 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 18902
% 59.45/59.80 Kept: 8793
% 59.45/59.80 Inuse: 331
% 59.45/59.80 Deleted: 12
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 28466
% 59.45/59.80 Kept: 11181
% 59.45/59.80 Inuse: 346
% 59.45/59.80 Deleted: 12
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 *** allocated 864960 integers for clauses
% 59.45/59.80 *** allocated 576640 integers for termspace/termends
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 41193
% 59.45/59.80 Kept: 14083
% 59.45/59.80 Inuse: 396
% 59.45/59.80 Deleted: 12
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 50836
% 59.45/59.80 Kept: 16887
% 59.45/59.80 Inuse: 442
% 59.45/59.80 Deleted: 16
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 *** allocated 864960 integers for termspace/termends
% 59.45/59.80 *** allocated 1297440 integers for clauses
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 57932
% 59.45/59.80 Kept: 19142
% 59.45/59.80 Inuse: 476
% 59.45/59.80 Deleted: 17
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 Resimplifying clauses:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 64016
% 59.45/59.80 Kept: 21161
% 59.45/59.80 Inuse: 542
% 59.45/59.80 Deleted: 187
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 74232
% 59.45/59.80 Kept: 23256
% 59.45/59.80 Inuse: 597
% 59.45/59.80 Deleted: 187
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 *** allocated 1297440 integers for termspace/termends
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 85885
% 59.45/59.80 Kept: 25968
% 59.45/59.80 Inuse: 622
% 59.45/59.80 Deleted: 187
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 *** allocated 1946160 integers for clauses
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 95414
% 59.45/59.80 Kept: 28462
% 59.45/59.80 Inuse: 642
% 59.45/59.80 Deleted: 187
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 113857
% 59.45/59.80 Kept: 31572
% 59.45/59.80 Inuse: 657
% 59.45/59.80 Deleted: 187
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 120040
% 59.45/59.80 Kept: 34050
% 59.45/59.80 Inuse: 672
% 59.45/59.80 Deleted: 187
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 127583
% 59.45/59.80 Kept: 36077
% 59.45/59.80 Inuse: 706
% 59.45/59.80 Deleted: 187
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 139513
% 59.45/59.80 Kept: 38411
% 59.45/59.80 Inuse: 708
% 59.45/59.80 Deleted: 187
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 *** allocated 1946160 integers for termspace/termends
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 145454
% 59.45/59.80 Kept: 41372
% 59.45/59.80 Inuse: 712
% 59.45/59.80 Deleted: 187
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 Resimplifying clauses:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 *** allocated 2919240 integers for clauses
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 153534
% 59.45/59.80 Kept: 45196
% 59.45/59.80 Inuse: 737
% 59.45/59.80 Deleted: 401
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 165192
% 59.45/59.80 Kept: 50481
% 59.45/59.80 Inuse: 777
% 59.45/59.80 Deleted: 401
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 174035
% 59.45/59.80 Kept: 52792
% 59.45/59.80 Inuse: 797
% 59.45/59.80 Deleted: 401
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 181510
% 59.45/59.80 Kept: 56917
% 59.45/59.80 Inuse: 817
% 59.45/59.80 Deleted: 401
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 190294
% 59.45/59.80 Kept: 59161
% 59.45/59.80 Inuse: 832
% 59.45/59.80 Deleted: 401
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 197123
% 59.45/59.80 Kept: 63393
% 59.45/59.80 Inuse: 842
% 59.45/59.80 Deleted: 401
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 Resimplifying clauses:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 *** allocated 4378860 integers for clauses
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 207588
% 59.45/59.80 Kept: 66196
% 59.45/59.80 Inuse: 872
% 59.45/59.80 Deleted: 448
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80 *** allocated 2919240 integers for termspace/termends
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 212865
% 59.45/59.80 Kept: 68904
% 59.45/59.80 Inuse: 882
% 59.45/59.80 Deleted: 448
% 59.45/59.80 Deletedinuse: 2
% 59.45/59.80
% 59.45/59.80 Resimplifying inuse:
% 59.45/59.80 Done
% 59.45/59.80
% 59.45/59.80
% 59.45/59.80 Intermediate Status:
% 59.45/59.80 Generated: 218746
% 59.45/59.80 Kept: 71644
% 59.45/59.80 Inuse: 897
% 175.36/175.74 Deleted: 448
% 175.36/175.74 Deletedinuse: 2
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 230181
% 175.36/175.74 Kept: 76867
% 175.36/175.74 Inuse: 922
% 175.36/175.74 Deleted: 448
% 175.36/175.74 Deletedinuse: 2
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 236434
% 175.36/175.74 Kept: 79282
% 175.36/175.74 Inuse: 942
% 175.36/175.74 Deleted: 448
% 175.36/175.74 Deletedinuse: 2
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 244640
% 175.36/175.74 Kept: 82058
% 175.36/175.74 Inuse: 967
% 175.36/175.74 Deleted: 448
% 175.36/175.74 Deletedinuse: 2
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying clauses:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 250668
% 175.36/175.74 Kept: 84170
% 175.36/175.74 Inuse: 997
% 175.36/175.74 Deleted: 644
% 175.36/175.74 Deletedinuse: 2
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 256493
% 175.36/175.74 Kept: 86175
% 175.36/175.74 Inuse: 1019
% 175.36/175.74 Deleted: 644
% 175.36/175.74 Deletedinuse: 2
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 263951
% 175.36/175.74 Kept: 88404
% 175.36/175.74 Inuse: 1042
% 175.36/175.74 Deleted: 644
% 175.36/175.74 Deletedinuse: 2
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 272099
% 175.36/175.74 Kept: 90465
% 175.36/175.74 Inuse: 1062
% 175.36/175.74 Deleted: 644
% 175.36/175.74 Deletedinuse: 2
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 281173
% 175.36/175.74 Kept: 92472
% 175.36/175.74 Inuse: 1085
% 175.36/175.74 Deleted: 644
% 175.36/175.74 Deletedinuse: 2
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 288293
% 175.36/175.74 Kept: 94694
% 175.36/175.74 Inuse: 1107
% 175.36/175.74 Deleted: 644
% 175.36/175.74 Deletedinuse: 2
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 297598
% 175.36/175.74 Kept: 97026
% 175.36/175.74 Inuse: 1122
% 175.36/175.74 Deleted: 644
% 175.36/175.74 Deletedinuse: 2
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 304278
% 175.36/175.74 Kept: 99863
% 175.36/175.74 Inuse: 1132
% 175.36/175.74 Deleted: 645
% 175.36/175.74 Deletedinuse: 3
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 *** allocated 4378860 integers for termspace/termends
% 175.36/175.74 *** allocated 6568290 integers for clauses
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 312865
% 175.36/175.74 Kept: 102816
% 175.36/175.74 Inuse: 1162
% 175.36/175.74 Deleted: 645
% 175.36/175.74 Deletedinuse: 3
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying clauses:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 320827
% 175.36/175.74 Kept: 104838
% 175.36/175.74 Inuse: 1187
% 175.36/175.74 Deleted: 1347
% 175.36/175.74 Deletedinuse: 3
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 328529
% 175.36/175.74 Kept: 106978
% 175.36/175.74 Inuse: 1211
% 175.36/175.74 Deleted: 1348
% 175.36/175.74 Deletedinuse: 3
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 349477
% 175.36/175.74 Kept: 110333
% 175.36/175.74 Inuse: 1231
% 175.36/175.74 Deleted: 1348
% 175.36/175.74 Deletedinuse: 3
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 359020
% 175.36/175.74 Kept: 112657
% 175.36/175.74 Inuse: 1256
% 175.36/175.74 Deleted: 1348
% 175.36/175.74 Deletedinuse: 3
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 367742
% 175.36/175.74 Kept: 114767
% 175.36/175.74 Inuse: 1281
% 175.36/175.74 Deleted: 1348
% 175.36/175.74 Deletedinuse: 3
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 376648
% 175.36/175.74 Kept: 116900
% 175.36/175.74 Inuse: 1306
% 175.36/175.74 Deleted: 1348
% 175.36/175.74 Deletedinuse: 3
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 383825
% 175.36/175.74 Kept: 119080
% 175.36/175.74 Inuse: 1351
% 175.36/175.74 Deleted: 1348
% 175.36/175.74 Deletedinuse: 3
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 390062
% 175.36/175.74 Kept: 121171
% 175.36/175.74 Inuse: 1391
% 175.36/175.74 Deleted: 1348
% 175.36/175.74 Deletedinuse: 3
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 397921
% 175.36/175.74 Kept: 123225
% 175.36/175.74 Inuse: 1426
% 175.36/175.74 Deleted: 1348
% 175.36/175.74 Deletedinuse: 3
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying clauses:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 411902
% 175.36/175.74 Kept: 125485
% 175.36/175.74 Inuse: 1451
% 175.36/175.74 Deleted: 1838
% 175.36/175.74 Deletedinuse: 3
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 Generated: 420054
% 175.36/175.74 Kept: 127523
% 175.36/175.74 Inuse: 1476
% 175.36/175.74 Deleted: 1849
% 175.36/175.74 Deletedinuse: 14
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74 Resimplifying inuse:
% 175.36/175.74 Done
% 175.36/175.74
% 175.36/175.74
% 175.36/175.74 Intermediate Status:
% 175.36/175.74 GeneratCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------