TSTP Solution File: SWW274+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW274+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 23:21:45 EDT 2022
% Result : Timeout 300.04s 300.54s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWW274+1 : TPTP v8.1.0. Released v5.2.0.
% 0.08/0.15 % Command : bliksem %s
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Mon Jun 6 04:12:16 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.01/1.61 *** allocated 10000 integers for termspace/termends
% 1.01/1.61 *** allocated 10000 integers for clauses
% 1.01/1.61 *** allocated 10000 integers for justifications
% 1.01/1.61 *** allocated 15000 integers for termspace/termends
% 1.01/1.61 *** allocated 22500 integers for termspace/termends
% 1.01/1.61 *** allocated 33750 integers for termspace/termends
% 1.01/1.61 Bliksem 1.12
% 1.01/1.61
% 1.01/1.61
% 1.01/1.61 Automatic Strategy Selection
% 1.01/1.61
% 1.01/1.61 *** allocated 50625 integers for termspace/termends
% 1.01/1.61 *** allocated 75937 integers for termspace/termends
% 1.01/1.61 *** allocated 113905 integers for termspace/termends
% 1.01/1.61 *** allocated 170857 integers for termspace/termends
% 1.01/1.61
% 1.01/1.61 Clauses:
% 1.01/1.61
% 1.01/1.61 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.01/1.61 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.01/1.61 tc_Complex_Ocomplex ) ) }.
% 1.01/1.61 { ! v_pa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.01/1.61 tc_Complex_Ocomplex ) ) }.
% 1.01/1.61 { ! v_k____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.01/1.61 { ! v_na____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Oorder(
% 1.01/1.61 tc_Complex_Ocomplex, X, v_pa____ ), v_na____ ) }.
% 1.01/1.61 { v_s____ = c_Polynomial_OpCons( tc_Complex_Ocomplex, v_k____,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.01/1.61 ) }.
% 1.01/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Oorder(
% 1.01/1.61 tc_Complex_Ocomplex, v_a____, v_pa____ ), v_na____ ) }.
% 1.01/1.61 { ! c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.61 { v_pa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 1.01/1.61 ( tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.01/1.61 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 1.01/1.61 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 1.01/1.61 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.01/1.61 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 1.01/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.01/1.61 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 1.01/1.61 , v_s____ ) }.
% 1.01/1.61 { v_qa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 1.01/1.61 ( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.01/1.61 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 1.01/1.61 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 1.01/1.61 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.01/1.61 tc_Complex_Ocomplex ) ) ) ) ), v_r____ ) }.
% 1.01/1.61 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_a____ ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.01/1.61 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_pa____ ) = v_na____ }.
% 1.01/1.61 { v_pa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 1.01/1.61 ( tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.01/1.61 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 1.01/1.61 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 1.01/1.61 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.01/1.61 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 1.01/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.01/1.61 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 1.01/1.61 , skol2 ) }.
% 1.01/1.61 { ! v_s____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.01/1.61 tc_Complex_Ocomplex ) ) }.
% 1.01/1.61 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 1.01/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 1.01/1.61 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.01/1.61 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 1.01/1.61 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 1.01/1.61 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.01/1.61 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 1.01/1.61 v_a____, v_pa____ ) ), v_pa____ ) }.
% 1.01/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.01/1.61 tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.01/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.01/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.01/1.61 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.01/1.61 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.01/1.61 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.61 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.01/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.61 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.61 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.61 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 1.01/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.61 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.01/1.61 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.61 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 1.01/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 1.01/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.01/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.01/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.01/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.01/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.01/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.01/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.01/1.61 { ! v_n = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.61 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_s____ ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.61 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) = v_n }.
% 1.01/1.61 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 1.01/1.61 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.01/1.61 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 1.01/1.61 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_qa____ ), X ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 1.01/1.61 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus
% 1.01/1.61 ( tc_Complex_Ocomplex, v_a____ ), c_Polynomial_OpCons(
% 1.01/1.61 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 1.01/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.01/1.61 ) ), v_qa____ ) }.
% 1.01/1.61 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.01/1.61 tc_Complex_Ocomplex ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.01/1.61 tc_Complex_Ocomplex ), v_pa____, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.01/1.61 ( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_qa____ ), v_na____ ) )
% 1.01/1.61 }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.01/1.61 ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.61 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.01/1.61 Z, T ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 1.01/1.61 ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.01/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 1.01/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.01/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 1.01/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.01/1.61 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.61 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.61 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 1.01/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.61 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.61 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.01/1.61 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.01/1.61 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.61 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.01/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 1.01/1.61 , Z, Y ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.01/1.61 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 1.01/1.61 ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.01/1.61 , Y ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.01/1.61 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.01/1.61 ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.61 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.01/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.01/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.01/1.61 tc_Nat_Onat ) ) = Y }.
% 1.01/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.01/1.61 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.01/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.01/1.61 }.
% 1.01/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.01/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.01/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.01/1.61 }.
% 1.01/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 1.01/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.01/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.01/1.61 }.
% 1.01/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 1.01/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.01/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.01/1.61 }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.01/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 1.01/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.01/1.61 ), T ), U ), Y ) }.
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.61 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 1.01/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.01/1.61 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 1.01/1.61 .
% 1.01/1.61 { ! class_Rings_Ocomm__semiring__1( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.01/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.01/1.61 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 1.01/1.61 .
% 1.01/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.01/1.61 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.01/1.61 c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.61 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.61 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.61 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.61 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.61 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.61 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.61 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.61 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.01/1.61 c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.61 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.01/1.61 ( X ) }.
% 1.01/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.01/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.01/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.01/1.61 .
% 1.01/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.01/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.01/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.61 tc_Nat_Onat ) }.
% 1.01/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.01/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.01/1.61 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.01/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.01/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.61 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.01/1.61 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.01/1.61 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.01/1.61 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.01/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.01/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.01/1.61 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.01/1.61 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.01/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.01/1.61 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.01/1.61 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.01/1.61 ( X, Y ) ) }.
% 1.01/1.61 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.01/1.61 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.01/1.61 ) ), Y ) }.
% 1.01/1.61 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.01/1.61 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.01/1.61 ( X, Y ) ) }.
% 1.01/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.61 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 }.
% 1.01/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.01/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.01/1.61 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 1.01/1.61 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.61 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 1.01/1.61 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.01/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.01/1.61 = c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.61 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 1.01/1.61 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.01/1.61 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.01/1.61 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.01/1.61 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.01/1.61 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.01/1.61 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.01/1.61 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.01/1.61 ), Y ) }.
% 1.01/1.61 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.01/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.01/1.61 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.01/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.01/1.61 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 1.01/1.61 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.01/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.61 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.01/1.61 ( X ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.61 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.01/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.61 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.01/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.61 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.01/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.61 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.01/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.61 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.01/1.61 ( X ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.61 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.01/1.61 ( X ) ), alpha1( X, Y, Z ), alpha36( X, Y, Z ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.01/1.61 ( X ) ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha36( X, Y, Z ),
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.01/1.61 ( X ) ) }.
% 1.01/1.61 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.01/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.01/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.01/1.61 ( X ), Y ), alpha36( X, Y, Z ) }.
% 1.01/1.61 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.01/1.61 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha1( X, Y, Z ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 1.01/1.61 , Z ), alpha37( X, Y, Z ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha37( X, Y, Z ),
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.61 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.01/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha37( X, Y, Z ) }.
% 1.01/1.61 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.01/1.61 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.01/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.01/1.61 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__semidom( X ),
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.01/1.61 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.01/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.01/1.61 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.01/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.01/1.61 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.01/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.61 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ), alpha38
% 1.01/1.61 ( X, Y, Z ) }.
% 1.01/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha3( X, Y, Z
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.01/1.61 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.01/1.61 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.01/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.01/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.01/1.61 ( X ), Y ), alpha38( X, Y, Z ) }.
% 1.01/1.61 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.01/1.61 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ) }.
% 1.01/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha4( X, Y, Z ), alpha39
% 1.01/1.61 ( X, Y, Z ) }.
% 1.01/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha4( X, Y, Z
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.01/1.61 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.01/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha39( X, Y, Z
% 1.01/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.01/1.61 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.01/1.61 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.01/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha39( X, Y, Z ) }.
% 1.01/1.61 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.01/1.61 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.01/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha4( X, Y, Z ) }.
% 1.01/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.01/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.01/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 1.01/1.61 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.01/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.01/1.61 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.01/1.61 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.01/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.01/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.01/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.01/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.61 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.01/1.61 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha40( X, Y, Z, T ) }.
% 1.01/1.61 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha5( X, Y, Z ) }.
% 1.01/1.61 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha40( X, Y, Z, T ), !
% 1.01/1.61 alpha5( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 1.01/1.61 { ! alpha40( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.01/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.01/1.61 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha40( X, Y, Z, T ) }.
% 1.01/1.61 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha40(
% 1.01/1.61 X, Y, Z, T ) }.
% 1.01/1.61 { ! alpha5( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.61 { Z = c_Groups_Ozero__class_Ozero( X ), alpha5( X, Y, Z ) }.
% 1.01/1.61 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha5( X, Y, Z ) }.
% 1.01/1.61 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha41( X, Y, Z, T ) }.
% 1.01/1.61 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.01/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha6( X, Y, T ) }.
% 1.01/1.61 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha41( X, Y, Z, T ), !
% 1.01/1.61 alpha6( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.01/1.61 { ! alpha41( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.01/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.01/1.61 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha41( X, Y, Z, T ) }.
% 1.01/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha41(
% 1.01/1.61 X, Y, Z, T ) }.
% 1.01/1.61 { ! alpha6( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.61 { Y = c_Groups_Ozero__class_Ozero( X ), alpha6( X, Y, Z ) }.
% 1.01/1.61 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha6( X, Y, Z ) }.
% 1.01/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.01/1.61 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.01/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.01/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 1.01/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.01/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.01/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.01/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.01/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.01/1.61 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.01/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.01/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.01/1.61 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.61 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.01/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.01/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.01/1.61 c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.01/1.62 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.01/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.01/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 1.01/1.62 ( X ) }.
% 1.01/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.01/1.62 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.01/1.62 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.01/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.01/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.01/1.62 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 1.01/1.62 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 1.01/1.62 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.62 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 1.01/1.62 { v_qa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 1.01/1.62 ( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 1.01/1.62 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.01/1.62 tc_Complex_Ocomplex ) ) ) ) ), skol3 ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 1.01/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 1.01/1.62 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 1.01/1.62 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.01/1.62 tc_Complex_Ocomplex ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder(
% 1.01/1.62 tc_Complex_Ocomplex, v_a____, v_pa____ ) ) ), v_pa____ ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.01/1.62 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 1.01/1.62 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.01/1.62 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.01/1.62 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.01/1.62 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 X ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 1.01/1.62 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.01/1.62 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.01/1.62 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 1.01/1.62 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { v_s____ = c_Polynomial_OpCons( tc_Complex_Ocomplex, skol4,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.01/1.62 ) }.
% 1.01/1.62 { v_s____ = c_Polynomial_OpCons( tc_Complex_Ocomplex, skol5,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.01/1.62 ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 1.01/1.62 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.01/1.62 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.01/1.62 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.01/1.62 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.01/1.62 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.01/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.62 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.01/1.62 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.01/1.62 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.01/1.62 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.01/1.62 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.01/1.62 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.01/1.62 , Y ), X ) }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.01/1.62 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.01/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.01/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Nat_Onat ) }.
% 1.01/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Nat_Onat ) }.
% 1.01/1.62 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.01/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.01/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.01/1.62 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.01/1.62 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.01/1.62 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.01/1.62 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.01/1.62 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.01/1.62 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.01/1.62 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.01/1.62 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.01/1.62 { ! c_Nat_OSuc( X ) = X }.
% 1.01/1.62 { ! X = c_Nat_OSuc( X ) }.
% 1.01/1.62 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.01/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.01/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.01/1.62 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.01/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.01/1.62 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.01/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.01/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.01/1.62 .
% 1.01/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.01/1.62 ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.01/1.62 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.01/1.62 , c_Nat_OSuc( X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.01/1.62 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.01/1.62 }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.01/1.62 c_Nat_OSuc( X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.01/1.62 ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.01/1.62 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.01/1.62 ), X ) ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.01/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.01/1.62 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.01/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.01/1.62 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.01/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.01/1.62 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.01/1.62 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 1.01/1.62 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 1.01/1.62 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.01/1.62 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.01/1.62 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.01/1.62 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.01/1.62 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.01/1.62 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 1.01/1.62 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.01/1.62 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 1.01/1.62 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.01/1.62 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 1.01/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.01/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 X ), Y ), Z = Y }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.01/1.62 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.01/1.62 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 1.01/1.62 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.01/1.62 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.01/1.62 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.01/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.01/1.62 .
% 1.01/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.01/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.01/1.62 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.01/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.01/1.62 .
% 1.01/1.62 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.01/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.01/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.01/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), Y ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.01/1.62 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.01/1.62 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.01/1.62 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.01/1.62 c_Polynomial_Odegree( X, Y ) }.
% 1.01/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.01/1.62 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.01/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.01/1.62 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.01/1.62 Y ) ) ), Y ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.01/1.62 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 1.01/1.62 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.01/1.62 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.01/1.62 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.01/1.62 Y ) ) ), Y ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.01/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.01/1.62 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.01/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.01/1.62 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.01/1.62 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.01/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.01/1.62 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.01/1.62 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.01/1.62 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.01/1.62 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.62 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.01/1.62 ) }.
% 1.01/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.01/1.62 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.01/1.62 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.01/1.62 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.01/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.01/1.62 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.01/1.62 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.01/1.62 ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 1.01/1.62 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.01/1.62 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.01/1.62 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.01/1.62 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.01/1.62 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 1.01/1.62 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.01/1.62 ( X ), Z, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X )
% 1.01/1.62 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree
% 1.01/1.62 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.01/1.62 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 1.01/1.62 ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.01/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), ! hAPP(
% 1.01/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, Z ), skol6( T, Z ) ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 1.01/1.62 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 1.01/1.62 ), Z ), X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), hAPP(
% 1.01/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol6( Y, Z ) ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 1.01/1.62 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 1.01/1.62 ), Z ), X ) ) }.
% 1.01/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.01/1.62 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.01/1.62 ( tc_Nat_Onat ) ) ) ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.01/1.62 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.01/1.62 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.01/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.01/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.01/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.01/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.01/1.62 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.01/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.01/1.62 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.01/1.62 X ) ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.01/1.62 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha7( X, Y ), Y = X }
% 1.01/1.62 .
% 1.01/1.62 { ! alpha7( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! alpha7( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! alpha7( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), alpha7( X, Y ) }.
% 1.01/1.62 { ! alpha8( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! alpha8( X, Y ), ! Y = X }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha8( X, Y ) }
% 1.01/1.62 .
% 1.01/1.62 { ! alpha8( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! alpha8( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), alpha8( X, Y ) }.
% 1.01/1.62 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.01/1.62 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, Y, X ), Y = X }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.01/1.62 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Nat_Onat, Y, Z ) }.
% 1.01/1.62 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Nat_Onat, Y, Z ) }.
% 1.01/1.62 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, Z, Y ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 1.01/1.62 , Z ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 1.01/1.62 Z, Y ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Nat_Onat, Y, Z ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, Z, Y ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { alpha105( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.01/1.62 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.01/1.62 { alpha105( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP(
% 1.01/1.62 hAPP( X, Y ), Z ) ) }.
% 1.01/1.62 { ! alpha105( X, Y, Z ), alpha106( X, Y, Z ), Z = Y }.
% 1.01/1.62 { ! alpha105( X, Y, Z ), alpha106( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ),
% 1.01/1.62 Z ) ) }.
% 1.01/1.62 { ! alpha106( X, Y, Z ), alpha105( X, Y, Z ) }.
% 1.01/1.62 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha105( X, Y, Z ) }.
% 1.01/1.62 { ! alpha106( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.01/1.62 }.
% 1.01/1.62 { ! alpha106( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.01/1.62 X, Y ), Z ) ), alpha106( X, Y, Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.01/1.62 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.01/1.62 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Y, Z ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.01/1.62 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.01/1.62 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.01/1.62 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.01/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.01/1.62 ), X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.01/1.62 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.01/1.62 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.01/1.62 .
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.01/1.62 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.01/1.62 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.01/1.62 }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.01/1.62 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.01/1.62 X ) ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.01/1.62 .
% 1.01/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.01/1.62 .
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.01/1.62 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.01/1.62 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.01/1.62 ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.01/1.62 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.01/1.62 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 1.01/1.62 }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.01/1.62 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.01/1.62 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( X ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.01/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.01/1.62 .
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.01/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.01/1.62 .
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.62 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( X ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.62 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( X ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.01/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha9( X, Y, Z, T ),
% 1.01/1.62 alpha42( X, Y, Z, T ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha42( X, Y, Z, T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.62 { ! alpha42( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! alpha42( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha42( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.01/1.62 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.01/1.62 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha9( X, Y, Z, T ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha10( X, Y, Z, T ),
% 1.01/1.62 alpha43( X, Y, Z, T ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z, T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha43( X, Y, Z, T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! alpha43( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! alpha43( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha43( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.01/1.62 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.01/1.62 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha10( X, Y, Z, T ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.01/1.62 .
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.01/1.62 .
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , Y, Z ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , Y, Z ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 1.01/1.62 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha11( X, Y, Z ), alpha44( X,
% 1.01/1.62 Y, Z ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha11( X, Y, Z
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha44( X, Y, Z
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.62 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.62 ), alpha44( X, Y, Z ) }.
% 1.01/1.62 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.01/1.62 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.01/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 ), alpha11( X, Y, Z ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha12( X, Y, Z ), alpha45
% 1.01/1.62 ( X, Y, Z ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha12( X, Y, Z
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha45( X, Y, Z
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.01/1.62 { ! alpha45( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! alpha45( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 ), alpha45( X, Y, Z ) }.
% 1.01/1.62 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.01/1.62 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.01/1.62 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.62 ), alpha12( X, Y, Z ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha13( X, Y ) }.
% 1.01/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.01/1.62 { ! alpha13( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.01/1.62 c_Nat_OSuc( X ) ) }.
% 1.01/1.62 { ! alpha13( X, Y ), Y = c_Nat_OSuc( skol7( Z, Y ) ) }.
% 1.01/1.62 { ! alpha13( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol7( X,
% 1.01/1.62 Y ), X ) }.
% 1.01/1.62 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.01/1.62 ), alpha13( X, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol8( X ) ) }.
% 1.01/1.62 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.01/1.62 ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.01/1.62 .
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.01/1.62 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.01/1.62 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.01/1.62 Y ), X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.01/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.01/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.01/1.62 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.01/1.62 ), X ) ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.01/1.62 ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.01/1.62 ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.01/1.62 ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.01/1.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.01/1.62 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.01/1.62 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 X ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.62 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 1.01/1.62 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.01/1.62 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.62 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.01/1.62 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 X ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.01/1.62 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.01/1.62 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.01/1.62 Y ), Z ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.62 Z, Y ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.62 Z, Y ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.01/1.62 Y ), Z ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.01/1.62 Y ), Z ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.62 Z, Y ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.01/1.62 Z ), Y ), alpha46( X, Y, Z, T ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.01/1.62 Z ), Y ), alpha67( X, Y, Z, T ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha46( X, Y, Z
% 1.01/1.62 , T ), ! alpha67( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.01/1.62 { ! alpha67( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), alpha81( X, Y, Z, T ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.01/1.62 , alpha67( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha81( X, Y, Z, T ), alpha67( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha81( X, Y, Z, T ), alpha93( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha81( X, Y, Z, T ), alpha14( X, Y, Z ) }.
% 1.01/1.62 { ! alpha93( X, Y, Z, T ), ! alpha14( X, Y, Z ), alpha81( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha93( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 alpha93( X, Y, Z, T ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha93( X, Y, Z, T )
% 1.01/1.62 }.
% 1.01/1.62 { ! alpha46( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.01/1.62 alpha46( X, Y, Z, T ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha46( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.62 , alpha14( X, Y, Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.01/1.62 , alpha14( X, Y, Z ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.62 Z, Y ) ), alpha47( X, Y, Z, T ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.62 Z, Y ) ), alpha68( X, Y, Z, T ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha47( X, Y, Z
% 1.01/1.62 , T ), ! alpha68( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.01/1.62 { ! alpha68( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y ), alpha82( X, Y, Z, T ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.01/1.62 , alpha68( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha82( X, Y, Z, T ), alpha68( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha82( X, Y, Z, T ), alpha94( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha82( X, Y, Z, T ), alpha15( X, Y, T ) }.
% 1.01/1.62 { ! alpha94( X, Y, Z, T ), ! alpha15( X, Y, T ), alpha82( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha94( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 alpha94( X, Y, Z, T ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha94( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha47( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 alpha47( X, Y, Z, T ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha47( X, Y, Z, T )
% 1.01/1.62 }.
% 1.01/1.62 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.62 , alpha15( X, Y, Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.62 , alpha15( X, Y, Z ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.01/1.62 ) ) = X }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.01/1.62 ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.01/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.01/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.01/1.62 ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.01/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.01/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.01/1.62 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.01/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.01/1.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , T, Y ), Z ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.01/1.62 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.01/1.62 ( X, Z, Y ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.01/1.62 ( X, Z, Y ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , T, Y ), Z ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , T, Y ), Z ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.01/1.62 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.01/1.62 ( X, Z, Y ) ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , T, Z ), Y ), alpha48( X, Y, Z, T ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.62 , T, Z ), Y ), alpha69( X, Y, Z, T ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha48( X, Y, Z
% 1.01/1.62 , T ), ! alpha69( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.01/1.62 { ! alpha69( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), alpha83( X, Y, Z, T ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.01/1.62 , alpha69( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha83( X, Y, Z, T ), alpha69( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha83( X, Y, Z, T ), alpha95( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha83( X, Y, Z, T ), alpha16( X, Y, Z ) }.
% 1.01/1.62 { ! alpha95( X, Y, Z, T ), ! alpha16( X, Y, Z ), alpha83( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha95( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 alpha95( X, Y, Z, T ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha95( X, Y, Z, T )
% 1.01/1.62 }.
% 1.01/1.62 { ! alpha48( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 1.01/1.62 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.01/1.62 alpha48( X, Y, Z, T ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha48( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.62 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.62 , alpha16( X, Y, Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 , Y ), alpha16( X, Y, Z ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.01/1.62 ( X, Z, Y ) ), alpha49( X, Y, Z, T ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.01/1.62 ( X, Z, Y ) ), alpha70( X, Y, Z, T ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha49( X, Y, Z
% 1.01/1.62 , T ), ! alpha70( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.01/1.62 { ! alpha70( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y ), alpha84( X, Y, Z, T ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.01/1.62 , alpha70( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha84( X, Y, Z, T ), alpha70( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha84( X, Y, Z, T ), alpha96( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha84( X, Y, Z, T ), alpha17( X, Y, T ) }.
% 1.01/1.62 { ! alpha96( X, Y, Z, T ), ! alpha17( X, Y, T ), alpha84( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha96( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.62 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 alpha96( X, Y, Z, T ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha96( X, Y, Z, T ) }.
% 1.01/1.62 { ! alpha49( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 1.01/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 alpha49( X, Y, Z, T ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha49( X, Y, Z, T )
% 1.01/1.62 }.
% 1.01/1.62 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.62 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.62 , alpha17( X, Y, Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.01/1.62 ) ), alpha17( X, Y, Z ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.01/1.62 c_Groups_Oone__class_Oone( X ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.01/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.01/1.62 ( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.01/1.62 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.01/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.01/1.62 = Y }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.01/1.62 = Y }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Nat_Onat ) ) = Y }.
% 1.01/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.01/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.01/1.62 ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.01/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.01/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.01/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.01/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 1.01/1.62 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 1.01/1.62 ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Nat_Onat, Z, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.01/1.62 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), Y ) }.
% 1.01/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.01/1.62 ), X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.01/1.62 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.01/1.62 X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.01/1.62 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.01/1.62 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.62 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.01/1.62 tc_Nat_Onat ), X ), Y ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Int_Oint, Z, X ) }.
% 1.01/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.01/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 1.01/1.62 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 1.01/1.62 ) }.
% 1.01/1.62 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ) ) }.
% 1.01/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.01/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.01/1.62 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.01/1.62 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.01/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.01/1.62 .
% 1.01/1.62 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Nat_Onat ), X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Nat_Onat ), Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.01/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.01/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.01/1.62 X, Y ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.01/1.62 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.01/1.62 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.01/1.62 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.01/1.62 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 , Y ) }.
% 1.01/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.01/1.62 , Y ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.01/1.62 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.01/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.62 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.01/1.62 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.01/1.62 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.01/1.62 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.01/1.62 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.01/1.62 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.01/1.62 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.01/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.01/1.62 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.01/1.62 ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.01/1.62 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.01/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.01/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.01/1.62 = Y }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.01/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.01/1.62 ) }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.01/1.62 ) }.
% 1.01/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( X ) }.
% 1.01/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Y ) }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 = Y }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.01/1.62 ) }.
% 1.01/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.01/1.62 = Y }.
% 1.01/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.01/1.62 = Y }.
% 1.01/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.01/1.62 = Y }.
% 1.01/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.01/1.62 = Y }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.62 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.62 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.01/1.62 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, Y ), Z ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.01/1.62 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, Z ), Y ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.01/1.62 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.01/1.62 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.01/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.01/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( X ) ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.01/1.62 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , Z, Y ) }.
% 1.01/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.01/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, Y ), Y ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.62 ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 ) }.
% 1.01/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.01/1.62 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ),
% 1.01/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ),
% 1.01/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 1.01/1.62 c_Polynomial_Odegree( X, Y ) ) }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.01/1.62 , Y ) }.
% 1.01/1.62 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.01/1.62 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.01/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.01/1.62 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.01/1.62 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.01/1.62 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.01/1.62 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.01/1.62 ) ) }.
% 1.01/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.01/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.01/1.62 hAPP( Y, U ) ) }.
% 1.01/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.01/1.62 ( Z, skol9( X, Y, Z ) ), hAPP( Y, skol9( X, Y, Z ) ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.01/1.62 ( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.01/1.62 ( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.01/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.01/1.62 hAPP( Y, U ) ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.01/1.62 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.01/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.01/1.62 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.01/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.01/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.01/1.62 hAPP( Y, U ) ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.01/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.01/1.62 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.01/1.62 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.01/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.01/1.62 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.01/1.62 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.01/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.01/1.62 , ! Y = Z }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.01/1.62 , ! Z = Y }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.01/1.62 , ! Z = Y }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.01/1.62 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.01/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.62 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 Y ), ! Z = Y }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.62 Z ), ! Z = Y }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.62 Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Int_Oint, Y, X ), X = Y }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 1.01/1.62 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Int_Oint, Y, X ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.01/1.62 ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.01/1.62 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), !
% 1.01/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ),
% 1.01/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.01/1.62 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.62 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.01/1.62 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.01/1.62 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.01/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.01/1.62 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.01/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.01/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.01/1.62 ( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.62 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.01/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.01/1.62 , ! Z = Y }.
% 1.01/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.62 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.01/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.01/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.62 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.01/1.62 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 1.01/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.01/1.62 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__field( X ),
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.01/1.62 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__field( X ),
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.01/1.62 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.01/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.01/1.62 ( tc_Int_Oint ) }.
% 1.01/1.62 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.01/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.01/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.01/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.01/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.01/1.62 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.01/1.62 .
% 1.01/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.01/1.62 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.01/1.62 }.
% 1.01/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.01/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.01/1.62 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.01/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.01/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.01/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.01/1.62 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.01/1.62 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.01/1.62 .
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.01/1.62 ( tc_Int_Oint ) ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Int_Oint ), X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.01/1.62 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.01/1.62 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.01/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.01/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.01/1.62 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.01/1.62 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.01/1.62 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.01/1.62 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.01/1.62 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.01/1.62 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__field( X ),
% 1.01/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.01/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.01/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.01/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 1.01/1.62 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 1.01/1.62 ) ) }.
% 1.01/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.01/1.62 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 1.01/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.62 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 1.01/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 1.01/1.62 .
% 1.01/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Int_Oint ) ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Int_Oint ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.01/1.62 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Int_Oint, X, Y ) }.
% 1.01/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.01/1.62 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.01/1.62 ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.01/1.62 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.01/1.62 alpha18( X, Y, Z ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.01/1.62 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! alpha18( X, Y, Z ),
% 1.01/1.62 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.01/1.62 { ! alpha18( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.01/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.01/1.62 alpha18( X, Y, Z ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.01/1.62 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.01/1.62 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.01/1.62 .
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.01/1.62 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.01/1.62 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 1.01/1.62 ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.01/1.62 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Int_Oint, X, Y ) }.
% 1.01/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.01/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.01/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.01/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.01/1.62 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 1.01/1.62 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 1.01/1.62 X, Z ), Y ) ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.01/1.62 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.01/1.62 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.01/1.62 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.01/1.62 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.01/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.01/1.62 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.01/1.62 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.01/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.01/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.01/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.01/1.62 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 1.01/1.62 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 1.01/1.62 hAPP( Z, Y ) ) }.
% 1.01/1.62 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.01/1.62 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.01/1.62 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 1.01/1.62 ) ) }.
% 1.01/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, Y ), Z = Y }.
% 1.01/1.62 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.01/1.62 ( X, Y ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 1.01/1.62 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.01/1.62 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.01/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 1.01/1.62 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 1.01/1.62 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.01/1.62 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 1.01/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.01/1.62 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 1.01/1.62 ( X ) ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol10( Z, Y ) ) ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 1.01/1.62 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 1.01/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Int_Oint, skol10( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 1.01/1.62 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 1.01/1.62 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 1.01/1.62 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.01/1.62 , Z ), X ) ) ) ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.01/1.62 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 1.01/1.62 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.01/1.62 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 1.01/1.62 .
% 1.01/1.62 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.01/1.62 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.01/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 1.01/1.62 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 1.01/1.62 .
% 1.01/1.62 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.01/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.01/1.62 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 1.01/1.62 ) }.
% 1.01/1.62 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.01/1.62 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.01/1.62 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.62 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 1.01/1.62 }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 1.01/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 1.01/1.62 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.01/1.62 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.62 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.62 }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.01/1.62 .
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.01/1.62 .
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.01/1.62 .
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 1.01/1.62 .
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 1.01/1.62 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.01/1.62 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 1.01/1.62 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.01/1.62 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 1.01/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 1.01/1.62 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 1.01/1.62 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.01/1.62 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.62 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.62 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.62 c_Groups_Oone__class_Oone( X ) ) }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 1.01/1.62 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 1.01/1.62 }.
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.01/1.62 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.01/1.62 .
% 1.01/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 1.01/1.62 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 1.01/1.62 }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.62 skol11( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( X, skol11( X, T, U ),
% 1.01/1.62 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.01/1.62 , Y ) }.
% 1.01/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.62 c_Groups_Otimes__class_Otimes( X ), skol11( X, Y, Z ) ), Z ), Y ),
% 1.01/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.01/1.62 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 1.01/1.62 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Nat_Onat ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.01/1.62 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.01/1.62 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.01/1.62 }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.01/1.62 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.01/1.62 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.01/1.62 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.01/1.62 ) }.
% 1.01/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.01/1.62 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Int_Oint ) }.
% 1.01/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 1.01/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.01/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 1.01/1.62 tc_Int_Oint ) ) }.
% 1.01/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.01/1.62 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.01/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.01/1.62 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.01/1.62 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.01/1.62 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 1.01/1.62 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.01/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.01/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 1.01/1.62 , Y ) }.
% 1.01/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.62 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 1.01/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = c_Nat_OSuc(
% 1.01/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.01/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 1.01/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.01/1.63 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Nat_Onat ) ) = Z }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.01/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.01/1.63 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.01/1.63 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.01/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.01/1.63 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.01/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.01/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.01/1.63 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.01/1.63 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.01/1.63 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.01/1.63 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.01/1.63 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.01/1.63 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 1.01/1.63 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.01/1.63 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.01/1.63 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.01/1.63 ( X, T, Y ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.01/1.63 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.01/1.63 , Y, Z ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.01/1.63 ( X, Z, Y ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.01/1.63 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.01/1.63 , T, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.01/1.63 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.01/1.63 , Y, T ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.01/1.63 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.01/1.63 , T, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.63 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.01/1.63 , T ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.01/1.63 ( X, Z, Y ) }.
% 1.01/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.01/1.63 ( X, Z, Y ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.01/1.63 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.01/1.63 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 Z, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 Y, Z ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.63 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.01/1.63 .
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.63 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.01/1.63 .
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.63 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.01/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.63 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.01/1.63 ) }.
% 1.01/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.01/1.63 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 ) }.
% 1.01/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.01/1.63 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.63 ) }.
% 1.01/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.63 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.01/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.01/1.63 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.01/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.01/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.01/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.01/1.63 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.01/1.63 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.01/1.63 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.63 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.01/1.63 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.63 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.63 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.01/1.63 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 1.01/1.63 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 1.01/1.63 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.01/1.63 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.01/1.63 , Y, T ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.01/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.01/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.01/1.63 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 1.01/1.63 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 1.01/1.63 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Int_Oint, Z, Y ) ) }.
% 1.01/1.63 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 1.01/1.63 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 1.01/1.63 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 1.01/1.63 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 1.01/1.63 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.01/1.63 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.01/1.63 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.01/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 1.01/1.63 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.01/1.63 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.01/1.63 c_Polynomial_Ocoeff( X, Y ) }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.01/1.63 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol12( X
% 1.01/1.63 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol12( X, Y, Z ) ), Z =
% 1.01/1.63 Y }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.01/1.63 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.01/1.63 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.01/1.63 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.01/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 Y, T ), Z = Y }.
% 1.01/1.63 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 T, Y ), Z = Y }.
% 1.01/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 T, Y ), Z = Y }.
% 1.01/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 Y, Z ), T = Y }.
% 1.01/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 Y, Z ) }.
% 1.01/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 T, Y ), Z = Y }.
% 1.01/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 T, Y ) }.
% 1.01/1.63 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.63 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.01/1.63 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.01/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.01/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.01/1.63 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.01/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.01/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.01/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.01/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.01/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.63 { ! class_RealVector_Oreal__normed__field( X ),
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 1.01/1.63 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 1.01/1.63 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.01/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.01/1.63 ) ) }.
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.01/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.01/1.63 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.01/1.63 ) }.
% 1.01/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.01/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.01/1.63 ), ! U = T }.
% 1.01/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.01/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.01/1.63 ), ! Z = Y }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.01/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.01/1.63 ) ), Z ) }.
% 1.01/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.01/1.63 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.01/1.63 ), U = Z, T = Y }.
% 1.01/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.01/1.63 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.01/1.63 ) }.
% 1.01/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.01/1.63 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.01/1.63 ) }.
% 1.01/1.63 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.01/1.63 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.01/1.63 ) ), T ), Y ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.01/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.01/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.01/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.01/1.63 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.01/1.63 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.01/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.01/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.01/1.63 ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), T ), c_Int_Onumber__class_Onumber__of( X, Y ) ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Y ) ) ) }.
% 1.01/1.63 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 T ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 T ) ), Y ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.01/1.63 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) =
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( X, c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 Y ) ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, c_Groups_Ouminus__class_Ouminus(
% 1.01/1.63 tc_Int_Oint, Y ) ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 1.01/1.63 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 1.01/1.63 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.01/1.63 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.01/1.63 X, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.01/1.63 X, Z, Y ) }.
% 1.01/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.01/1.63 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.01/1.63 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.63 , Y ) ) }.
% 1.01/1.63 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.01/1.63 W ) ), U ), Y ) }.
% 1.01/1.63 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.01/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.01/1.63 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), Z ), U ), Y ) }.
% 1.01/1.63 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.01/1.63 Z ) ), U ), T ) = Y }.
% 1.01/1.63 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.01/1.63 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), Z ), U ), Y ) }.
% 1.01/1.63 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.01/1.63 Z ) ), Y ) ) }.
% 1.01/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.01/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.01/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.01/1.63 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.01/1.63 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.01/1.63 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.01/1.63 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.01/1.63 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.01/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.01/1.63 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.01/1.63 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.01/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.01/1.63 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.01/1.63 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.01/1.63 ( X, Z ) }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.63 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.01/1.63 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.63 Z ) = Y }.
% 1.01/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.01/1.63 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.01/1.63 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.01/1.63 ( X, Y ) }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.01/1.63 X ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.01/1.63 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.01/1.63 ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 Z ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), Z ) ) ), Y ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, hAPP
% 1.01/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 1.01/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.01/1.63 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 T ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.01/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 T ) ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 1.01/1.63 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.01/1.63 Z ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.01/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 1.01/1.63 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 1.01/1.63 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.01/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.01/1.63 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.01/1.63 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.01/1.63 Y ) ) = Y }.
% 1.01/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 Z, Y ) ) = Y }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 1.01/1.63 X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ), Z ) }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.01/1.63 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 1.01/1.63 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.01/1.63 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.01/1.63 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 1.01/1.63 .
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.01/1.63 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.01/1.63 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.01/1.63 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.63 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 1.01/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.01/1.63 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.01/1.63 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 }.
% 1.01/1.63 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.01/1.63 ) ) }.
% 1.01/1.63 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.01/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 1.01/1.63 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.01/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.01/1.63 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.01/1.63 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 1.01/1.63 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.01/1.63 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 X, Z ) ) = Y, alpha50( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 X, Z ) ) = Y, alpha19( X, Y, Z ) }.
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.01/1.63 alpha50( X, Y, Z, T ), ! alpha19( X, Y, Z ),
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 X, Z ) ) = Y }.
% 1.01/1.63 { ! alpha50( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Z ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), T = hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Z ) ) }.
% 1.01/1.63 { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 1.01/1.63 ( X ), alpha50( X, Y, Z, T ) }.
% 1.01/1.63 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha50( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha19( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Z ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.01/1.63 .
% 1.01/1.63 { c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ), alpha19( X, Y, Z ) }.
% 1.01/1.63 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha19( X, Y, Z ) }.
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ), alpha51( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ), alpha20( X, Y, Z ) }.
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.01/1.63 alpha51( X, Y, Z, T ), ! alpha20( X, Y, Z ),
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 1.01/1.63 { ! alpha51( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.01/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) }.
% 1.01/1.63 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha51( X, Y, Z, T ) }.
% 1.01/1.63 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), alpha51( X, Y, Z, T ) }
% 1.01/1.63 .
% 1.01/1.63 { ! alpha20( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) }.
% 1.01/1.63 { Z = c_Groups_Ozero__class_Ozero( X ), alpha20( X, Y, Z ) }.
% 1.01/1.63 { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 1.01/1.63 ( X ), alpha20( X, Y, Z ) }.
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ) =
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha52( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ) =
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha21( X, Y, T ) }.
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.01/1.63 alpha52( X, Y, Z, T ), ! alpha21( X, Y, T ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ) =
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.01/1.63 { ! alpha52( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.01/1.63 ( c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X
% 1.01/1.63 , T ) ), Y ) = Z }.
% 1.01/1.63 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha52( X, Y, Z, T ) }.
% 1.01/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) = Z, alpha52( X, Y, Z, T
% 1.01/1.63 ) }.
% 1.01/1.63 { ! alpha21( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) }.
% 1.01/1.63 { Y = c_Groups_Ozero__class_Ozero( X ), alpha21( X, Y, Z ) }.
% 1.01/1.63 { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 1.01/1.63 ( X ), alpha21( X, Y, Z ) }.
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T
% 1.01/1.63 = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Y ) ), alpha53( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T
% 1.01/1.63 = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Y ) ), alpha22( X, Y, T ) }.
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.01/1.63 alpha53( X, Y, Z, T ), ! alpha22( X, Y, T ), T =
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 X, Y ) ) }.
% 1.01/1.63 { ! alpha53( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Y ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Y ) ) = Z }.
% 1.01/1.63 { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 1.01/1.63 ( X ), alpha53( X, Y, Z, T ) }.
% 1.01/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ) = Z, alpha53( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha22( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Y ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.01/1.63 .
% 1.01/1.63 { c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ), alpha22( X, Y, Z ) }.
% 1.01/1.63 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha22( X, Y, Z ) }.
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.01/1.63 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.63 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.01/1.63 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.63 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.01/1.63 ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.63 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.01/1.63 ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.01/1.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.01/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.63 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 }.
% 1.01/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 }.
% 1.01/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.01/1.63 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.01/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.01/1.63 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.01/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.01/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.01/1.63 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.01/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.01/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.01/1.63 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.01/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.01/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.63 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.01/1.63 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.01/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.01/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.01/1.63 X, W, Z ) ), U ), T ), Y ) }.
% 1.01/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.01/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), Z ), U ), Y ) ) }.
% 1.01/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.01/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.01/1.63 ( X, Z, W ) ), U ), Y ) ) }.
% 1.01/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.01/1.63 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.01/1.63 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.01/1.63 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.01/1.63 hAPP( Z, skol13( U, W, Z ) ) ) }.
% 1.01/1.63 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.01/1.63 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 1.01/1.63 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol13( X
% 1.01/1.63 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.01/1.63 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 1.01/1.63 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 1.01/1.63 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol18( X,
% 1.01/1.63 Y, Z ) ) ) ) }.
% 1.01/1.63 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.01/1.63 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.01/1.63 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.01/1.63 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.01/1.63 .
% 1.01/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.01/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 1.01/1.63 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 1.01/1.63 .
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.01/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 1.01/1.63 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 1.01/1.63 .
% 1.01/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.01/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ) ) ), Y ) = hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Z ) ) ), Y ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.01/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.01/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.01/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.01/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.01/1.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.01/1.63 }.
% 1.01/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.01/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.01/1.63 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.01/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.01/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.01/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.01/1.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.01/1.63 }.
% 1.01/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.63 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.01/1.63 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.01/1.63 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.01/1.63 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.01/1.63 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.01/1.63 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.01/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.01/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.01/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.01/1.63 .
% 1.01/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.01/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.01/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), ! c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 tc_Nat_Onat, Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.01/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.01/1.63 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.63 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 1.01/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.01/1.63 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.01/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.01/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.01/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.01/1.63 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.01/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.01/1.63 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.01/1.63 , Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.01/1.63 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.01/1.63 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.01/1.63 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 X, Z ) ), Y ), alpha54( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 X, Z ) ), Y ), alpha71( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! alpha54( X, Y, Z, T ), ! alpha71( X, Y, Z, T )
% 1.01/1.63 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 1.01/1.63 , c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 1.01/1.63 { ! alpha71( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 1.01/1.63 ) ), alpha85( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha71( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha85( X, Y, Z, T ), alpha71( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha85( X, Y, Z, T ), alpha97( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha85( X, Y, Z, T ), alpha23( X, Y, Z ) }.
% 1.01/1.63 { ! alpha97( X, Y, Z, T ), ! alpha23( X, Y, Z ), alpha85( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha97( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Z ) ), T ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 1.01/1.63 ), c_Groups_Ozero__class_Ozero( X ) ), alpha97( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Z ) ), T ), alpha97( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha54( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Z ) ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha54( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Z ) ) ), alpha54( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 , Y ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha23( X, Y, Z ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.01/1.63 , alpha23( X, Y, Z ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha55( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha72( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! alpha55( X, Y, Z, T ), ! alpha72( X, Y, Z, T )
% 1.01/1.63 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 1.01/1.63 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.01/1.63 { ! alpha72( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), alpha86( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.01/1.63 , alpha72( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha86( X, Y, Z, T ), alpha72( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha86( X, Y, Z, T ), alpha98( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha86( X, Y, Z, T ), alpha24( X, Y, Z ) }.
% 1.01/1.63 { ! alpha98( X, Y, Z, T ), ! alpha24( X, Y, Z ), alpha86( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha98( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), T ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.63 alpha98( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 Y ) ), Z ), T ), alpha98( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha55( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.01/1.63 alpha55( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 Y ) ), Z ) ), alpha55( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 1.01/1.63 ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.63 , alpha24( X, Y, Z ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha24( X, Y, Z ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 1.01/1.63 ( X, Z, Y ) ), alpha56( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 1.01/1.63 ( X, Z, Y ) ), alpha73( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! alpha56( X, Y, Z, T ), ! alpha73( X, Y, Z, T )
% 1.01/1.63 , c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.01/1.63 { ! alpha73( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), alpha87( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.01/1.63 , alpha73( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha87( X, Y, Z, T ), alpha73( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha87( X, Y, Z, T ), alpha99( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha87( X, Y, Z, T ), alpha25( X, Y, T ) }.
% 1.01/1.63 { ! alpha99( X, Y, Z, T ), ! alpha25( X, Y, T ), alpha87( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha99( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.63 alpha99( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 T ) ), Y ) ), alpha99( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha56( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ), Z ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.63 alpha56( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 T ) ), Y ), Z ), alpha56( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.63 , alpha25( X, Y, Z ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha25( X, Y, Z ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 X, Y ) ) ), alpha57( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 X, Y ) ) ), alpha74( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! alpha57( X, Y, Z, T ), ! alpha74( X, Y, Z, T )
% 1.01/1.63 , c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X
% 1.01/1.63 , Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 1.01/1.63 { ! alpha74( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 1.01/1.63 ) ), alpha88( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha74( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha88( X, Y, Z, T ), alpha74( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha88( X, Y, Z, T ), alpha100( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha88( X, Y, Z, T ), alpha26( X, Y, T ) }.
% 1.01/1.63 { ! alpha100( X, Y, Z, T ), ! alpha26( X, Y, T ), alpha88( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha100( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Y ) ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.01/1.63 ), c_Groups_Ozero__class_Ozero( X ) ), alpha100( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Y ) ) ), alpha100( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha57( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Y ) ), Z ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha57( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Y ) ), Z ), alpha57( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha26( X, Y, Z ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.63 , alpha26( X, Y, Z ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.01/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.63 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.01/1.63 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.01/1.63 ), Y ) }.
% 1.01/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), !
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 1.01/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.01/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.01/1.63 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.01/1.63 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.01/1.63 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.01/1.63 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.01/1.63 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.01/1.63 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.01/1.63 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.01/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 1.01/1.63 ( X ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 X, Z ) ), Y ), alpha58( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 X, Z ) ), Y ), alpha75( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! alpha58( X, Y, Z, T ), ! alpha75( X, Y, Z, T )
% 1.01/1.63 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 1.01/1.63 X, T, c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 1.01/1.63 { ! alpha75( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 1.01/1.63 ) ), alpha89( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha75( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha89( X, Y, Z, T ), alpha75( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha89( X, Y, Z, T ), alpha101( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha89( X, Y, Z, T ), alpha27( X, Y, Z ) }.
% 1.01/1.63 { ! alpha101( X, Y, Z, T ), ! alpha27( X, Y, Z ), alpha89( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha101( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Z ) ), T ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 1.01/1.63 ), c_Groups_Ozero__class_Ozero( X ) ), alpha101( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Z ) ), T ), alpha101( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha58( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Z ) ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha58( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Z ) ) ), alpha58( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.01/1.63 X ), Y ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha27( X, Y, Z ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 , Y ), alpha27( X, Y, Z ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha59( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha76( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! alpha59( X, Y, Z, T ), ! alpha76( X, Y, Z, T )
% 1.01/1.63 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 1.01/1.63 X, T, Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.01/1.63 { ! alpha76( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), alpha90( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.01/1.63 , alpha76( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha90( X, Y, Z, T ), alpha76( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha90( X, Y, Z, T ), alpha102( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha90( X, Y, Z, T ), alpha28( X, Y, Z ) }.
% 1.01/1.63 { ! alpha102( X, Y, Z, T ), ! alpha28( X, Y, Z ), alpha90( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha102( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), T ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.63 alpha102( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 Y ) ), Z ), T ), alpha102( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha59( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 1.01/1.63 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.01/1.63 alpha59( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 Y ) ), Z ) ), alpha59( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.63 , c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 Y ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.63 , alpha28( X, Y, Z ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.01/1.63 , c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha28( X, Y, Z ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 1.01/1.63 ( X, Z, Y ) ), alpha60( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 1.01/1.63 ( X, Z, Y ) ), alpha77( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! alpha60( X, Y, Z, T ), ! alpha77( X, Y, Z, T )
% 1.01/1.63 , c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.01/1.63 { ! alpha77( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), alpha91( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.01/1.63 , alpha77( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha91( X, Y, Z, T ), alpha77( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha91( X, Y, Z, T ), alpha103( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha91( X, Y, Z, T ), alpha29( X, Y, T ) }.
% 1.01/1.63 { ! alpha103( X, Y, Z, T ), ! alpha29( X, Y, T ), alpha91( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha103( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.63 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.01/1.63 alpha103( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 T ) ), Y ) ), alpha103( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha60( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 1.01/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ), Z ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.01/1.63 alpha60( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 T ) ), Y ), Z ), alpha60( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.01/1.63 , c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero(
% 1.01/1.63 X ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.01/1.63 , alpha29( X, Y, Z ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha29( X, Y, Z ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 X, Y ) ) ), alpha61( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 X, Y ) ) ), alpha78( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.01/1.63 class_Int_Onumber( X ), ! alpha61( X, Y, Z, T ), ! alpha78( X, Y, Z, T )
% 1.01/1.63 , c_Orderings_Oord__class_Oless__eq( X, T,
% 1.01/1.63 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 1.01/1.63 X, Y ) ) ) }.
% 1.01/1.63 { ! alpha78( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 1.01/1.63 ) ), alpha92( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha78( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha92( X, Y, Z, T ), alpha78( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha92( X, Y, Z, T ), alpha104( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha92( X, Y, Z, T ), alpha30( X, Y, T ) }.
% 1.01/1.63 { ! alpha104( X, Y, Z, T ), ! alpha30( X, Y, T ), alpha92( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha104( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Y ) ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.01/1.63 ), c_Groups_Ozero__class_Ozero( X ) ), alpha104( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Y ) ) ), alpha104( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha61( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Y ) ), Z ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha61( X, Y, Z, T ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.01/1.63 ( X, Y ) ), Z ), alpha61( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 1.01/1.63 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha30( X, Y, Z ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.01/1.63 ) ), alpha30( X, Y, Z ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.01/1.63 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.01/1.63 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.01/1.63 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.01/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.01/1.63 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.01/1.63 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.01/1.63 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.01/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.01/1.63 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.01/1.63 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 1.01/1.63 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.01/1.63 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.01/1.63 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 1.01/1.63 }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.01/1.63 , alpha79( X, Y, Z, T ) }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha79( X, Y, Z, T ),
% 1.01/1.63 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.01/1.63 { ! alpha79( X, Y, Z, T ), alpha31( X, Z, T ) }.
% 1.01/1.63 { ! alpha79( X, Y, Z, T ), alpha62( X, Y, T ) }.
% 1.01/1.63 { ! alpha31( X, Z, T ), ! alpha62( X, Y, T ), alpha79( X, Y, Z, T ) }.
% 1.01/1.63 { ! alpha62( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ), alpha80( X, Y, Z ) }.
% 1.01/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha62( X
% 1.01/1.63 , Y, Z ) }.
% 1.01/1.63 { ! alpha80( X, Y, Z ), alpha62( X, Y, Z ) }.
% 1.01/1.63 { ! alpha80( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.63 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.01/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha80( X
% 1.01/1.63 , Y, Z ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.01/1.63 ), c_Polynomial_Odegree( X, Z ) ), alpha80( X, Y, Z ) }.
% 1.01/1.63 { ! alpha31( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha31( X,
% 1.01/1.63 Y, Z ) }.
% 1.01/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha31( X
% 1.01/1.63 , Y, Z ) }.
% 1.01/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.01/1.63 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 1.01/1.63 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.01/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.01/1.63 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.01/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.01/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.01/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.01/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.01/1.63 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Z, Y ) ) }.
% 1.01/1.63 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha32( X, Y ),
% 1.01/1.63 alpha63( X, Y ) }.
% 1.01/1.63 { ! alpha32( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.01/1.63 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.01/1.63 { ! alpha63( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.01/1.63 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.01/1.63 { ! alpha63( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.63 { ! alpha63( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Nat_Onat ) ) }.
% 1.01/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha63( X, Y ) }.
% 1.01/1.63 { ! alpha32( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Nat_Onat ) ) }.
% 1.01/1.63 { ! alpha32( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha32( X, Y ) }.
% 1.01/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha33( X, Y ), alpha64( X
% 1.01/1.63 , Y ) }.
% 1.01/1.63 { ! alpha33( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.01/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.63 { ! alpha64( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.01/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.01/1.63 { ! alpha64( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.63 { ! alpha64( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Nat_Onat ) ) }.
% 1.01/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha64( X, Y ) }.
% 1.01/1.63 { ! alpha33( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Nat_Onat ) ) }.
% 1.01/1.63 { ! alpha33( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha33( X, Y ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.63 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Y, X ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.01/1.63 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Y, X ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Int_Oint, X, Y ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol14( X, Y ) ) ) }.
% 1.01/1.63 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.01/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.01/1.63 .
% 1.01/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.01/1.63 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.01/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.01/1.63 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol15( X, Y ) ) }.
% 1.01/1.63 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.01/1.63 , X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.01/1.63 .
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.01/1.63 .
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.01/1.63 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.01/1.63 .
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.01/1.63 .
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.01/1.63 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.01/1.63 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.01/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.01/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.01/1.63 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.01/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.01/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Nat_Onat ), X ) = X }.
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.01/1.63 ( tc_Nat_Onat ) ) = X }.
% 1.01/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Int_Oint ), X ) = X }.
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.01/1.63 ( tc_Int_Oint ) ) = X }.
% 1.01/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.01/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.01/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.01/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.01/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.01/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.01/1.63 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.01/1.63 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.01/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.01/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.01/1.63 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.01/1.63 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.01/1.63 { c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.01/1.63 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.01/1.63 = X }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.01/1.63 tc_Int_Oint ) ) ) }.
% 1.01/1.63 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.01/1.63 tc_Int_Oint ) ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Z, X ), Y ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.01/1.63 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.01/1.63 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.01/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.01/1.63 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.01/1.63 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.01/1.63 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Z, X ), Y ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Nat_Onat, Z, Y ), X ) }.
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.01/1.63 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.01/1.63 .
% 1.01/1.63 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.01/1.63 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.01/1.63 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.01/1.63 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.01/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.01/1.63 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.01/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.01/1.63 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.01/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 1.01/1.63 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 1.01/1.63 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.01/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.01/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.01/1.63 , Z ), X ) ), T ) ) }.
% 1.01/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.01/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 1.01/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Int_Oint, U, T ) ) }.
% 1.01/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 1.01/1.63 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.01/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.01/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.01/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.01/1.63 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Z ),
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.01/1.63 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Int_Oint, Z, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }.
% 1.01/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.01/1.63 , alpha34( X, Y, Z ) }.
% 1.01/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.01/1.63 , alpha65( X, Y, Z ) }.
% 1.01/1.63 { ! alpha34( X, Y, Z ), ! alpha65( X, Y, Z ), hBOOL( hAPP( Z,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.01/1.63 { ! alpha65( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.01/1.63 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.01/1.63 { ! hBOOL( hAPP( Z, skol16( T, U, Z ) ) ), alpha65( X, Y, Z ) }.
% 1.01/1.63 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol16( X, Y, Z ) ),
% 1.01/1.63 alpha65( X, Y, Z ) }.
% 1.01/1.63 { ! alpha34( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.01/1.63 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.01/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha34( X, Y, Z ) }
% 1.01/1.63 .
% 1.01/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha34
% 1.01/1.63 ( X, Y, Z ) }.
% 1.01/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.01/1.63 , ! alpha35( X, Y, Z ) }.
% 1.01/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.01/1.63 , ! alpha66( X, Y, Z ) }.
% 1.01/1.63 { alpha35( X, Y, Z ), alpha66( X, Y, Z ), hBOOL( hAPP( Z,
% 1.01/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.01/1.63 { ! alpha66( X, Y, Z ), ! hBOOL( hAPP( Z, skol17( T, U, Z ) ) ) }.
% 1.01/1.63 { ! alpha66( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.01/1.63 skol17( X, Y, Z ) ) }.
% 1.01/1.63 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.01/1.63 ) ), alpha66( X, Y, Z ) }.
% 1.01/1.63 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.01/1.63 }.
% 1.01/1.63 { ! alpha35( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.01/1.63 tc_Nat_Onat ) ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha35( X, Y, Z ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.01/1.63 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.01/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.01/1.63 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.01/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.01/1.63 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.01/1.63 }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.01/1.63 tc_Int_Oint ) ) ) }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.01/1.63 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.01/1.63 }.
% 1.01/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.01/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.01/1.63 tc_Int_Oint ) ), X ) }.
% 1.01/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.01/1.63 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.01/1.63 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.01/1.63 ( tc_fun( Y, X ) ) }.
% 1.01/1.63 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.01/1.63 ) ) }.
% 1.01/1.63 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.01/1.63 .
% 1.01/1.63 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.01/1.63 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.01/1.63 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.01/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.01/1.63 tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.01/1.63 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.01/1.63 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.01/1.63 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.01/1.63 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.01/1.63 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.01/1.63 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.01/1.63 { class_Power_Opower( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.01/1.63 { class_Int_Onumber( tc_Int_Oint ) }.
% 1.01/1.63 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.01/1.63 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.01/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.01/1.63 tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Int_Onumber( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.01/1.63 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.01/1.63 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.01/1.63 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.01/1.63 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.01/1.63 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.01/1.63 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.01/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.01/1.63 tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 1.01/1.63 { ! class_Rings_Oidom( X ),
% 1.01/1.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.01/1.63 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.01/1.63 ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.01/1.63 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.01/1.63 X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.01/1.63 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.01/1.63 ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.01/1.63 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.01/1.63 }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.01/1.63 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.01/1.63 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.01/1.63 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.01/1.63 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.01/1.63 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.01/1.63 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.01/1.63 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.01/1.63 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.01/1.63 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.01/1.63 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.01/1.63 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.01/1.63 ( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.01/1.63 ( tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber__ring(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.01/1.63 }.
% 1.01/1.63 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.01/1.63 ) ) }.
% 1.01/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.01/1.63 .
% 1.01/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber( tc_Polynomial_Opoly
% 1.01/1.63 ( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.01/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.01/1.63 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.01/1.63 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.01/1.63 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 1.01/1.63 tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.01/1.63 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 1.01/1.63 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 1.01/1.63 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.01/1.63 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.01/1.63 ) ) ), v_r____ ) ), v_na____ ) = hAPP( hAPP(
% 1.01/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 1.01/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly(
% 1.01/1.63 tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.01/1.63 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 1.01/1.63 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 1.01/1.63 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.01/1.63 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.01/1.63 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 1.01/1.63 , c_Polynomial_OpCons( tc_Complex_Ocomplex, v_k____,
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.01/1.63 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly(
% 1.01/1.63 tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.01/1.63 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 1.01/1.63 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex
% 1.01/1.63 , c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), v_k____ ),
% 1.01/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.01/1.63 ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 1.01/1.63 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 1.01/1.63 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 1.01/1.63 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.01/1.63 tc_Complex_Ocomplex ) ) ) ) ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.01/1.63 , v_na____, c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ )
% 1.01/1.63 ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 1.01/1.63 tc_Complex_Ocomplex ) ), v_r____ ), v_na____ ) ) ) }.
% 1.01/1.63
% 1.01/1.63 *** allocated 15000 integers for clauses
% 1.01/1.63 *** allocated 22500 integers for clauses
% 1.01/1.63 *** allocated 33750 integers for clauses
% 1.01/1.63 *** allocated 50625 integers for clauses
% 1.01/1.63 *** allocated 75937 integers for clauses
% 1.01/1.63 *** allocated 113905 integers for clauses
% 1.01/1.63 percentage equality = 0.232928, percentage horn = 0.887002
% 1.01/1.63 This is a problem with some equality
% 1.01/1.63
% 1.01/1.63
% 1.01/1.63
% 1.01/1.63 Options Used:
% 1.01/1.63
% 1.01/1.63 useres = 1
% 1.01/1.63 useparamod = 1
% 1.01/1.63 useeqrefl = 1
% 1.01/1.63 useeqfact = 1
% 1.01/1.63 usefactor = 1
% 1.01/1.63 usesimpsplitting = 0
% 1.01/1.63 usesimpdemod = 5
% 1.01/1.63 usesimpres = 3
% 1.01/1.63
% 1.01/1.63 resimpinuse = 1000
% 1.01/1.63 resimpclauses = 20000
% 1.01/1.63 substype = eqrewr
% 1.01/1.63 backwardsubs = 1
% 1.01/1.63 selectoldest = 5
% 1.01/1.63
% 1.01/1.63 litorderings [0] = split
% 1.01/1.63 litorderings [1] = extend the termordering, first sorting on arguments
% 1.01/1.63
% 1.01/1.63 termordering = kbo
% 1.01/1.63
% 1.01/1.63 litapriori = 0
% 1.01/1.63 termapriori = 1
% 1.01/1.63 litaposteriori = 0
% 1.01/1.63 termaposteriori = 0
% 1.01/1.63 demodaposteriori = 0
% 1.01/1.63 ordereqreflfact = 0
% 1.01/1.63
% 1.01/1.63 litselect = negord
% 1.01/1.63
% 1.01/1.63 maxweight = 15
% 1.01/1.63 maxdepth = 30000
% 1.01/1.63 maxlength = 115
% 1.01/1.63 maxnrvars = 195
% 1.01/1.63 excuselevel = 1
% 1.01/1.63 increasemaxweight = 1
% 1.01/1.63
% 1.01/1.63 maxselected = 10000000
% 1.01/1.63 maxnrclauses = 10000000
% 1.01/1.63
% 1.01/1.63 showgenerated = 0
% 1.01/1.63 showkept = 0
% 1.01/1.63 showselected = 0
% 1.01/1.63 showdeleted = 0
% 1.01/1.63 showresimp = 1
% 1.01/1.63 showstatus = 2000
% 1.01/1.63
% 1.01/1.63 prologoutput = 0
% 1.01/1.63 nrgoals = 5000000
% 1.01/1.63 totalproof = 1
% 1.01/1.63
% 1.01/1.63 Symbols occurring in the translation:
% 1.01/1.63
% 1.01/1.63 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.01/1.63 . [1, 2] (w:1, o:199, a:1, s:1, b:0),
% 1.01/1.63 ! [4, 1] (w:0, o:112, a:1, s:1, b:0),
% 1.01/1.63 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.01/1.63 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.01/1.63 hAPP [38, 2] (w:1, o:223, a:1, s:1, b:0),
% 1.01/1.63 v_qa____ [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.01/1.63 tc_Complex_Ocomplex [40, 0] (w:1, o:18, a:1, s:1, b:0),
% 1.01/1.63 tc_Polynomial_Opoly [41, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.01/1.63 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.01/1.63 v_pa____ [43, 0] (w:1, o:11, a:1, s:1, b:0),
% 1.01/1.63 v_k____ [44, 0] (w:1, o:19, a:1, s:1, b:0),
% 1.01/1.63 v_na____ [45, 0] (w:1, o:20, a:1, s:1, b:0),
% 1.01/1.63 tc_Nat_Onat [46, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.01/1.63 c_Polynomial_Oorder [48, 3] (w:1, o:250, a:1, s:1, b:0),
% 1.01/1.63 c_Orderings_Oord__class_Oless__eq [49, 3] (w:1, o:248, a:1, s:1, b:0)
% 1.01/1.63 ,
% 1.01/1.63 v_s____ [50, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.01/1.63 c_Polynomial_OpCons [51, 3] (w:1, o:251, a:1, s:1, b:0),
% 1.01/1.63 v_a____ [52, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.01/1.63 c_Groups_Otimes__class_Otimes [53, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.01/1.63 c_Power_Opower__class_Opower [54, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.01/1.63 c_Groups_Ouminus__class_Ouminus [55, 2] (w:1, o:225, a:1, s:1, b:0),
% 1.01/1.63
% 1.01/1.63 c_Groups_Oone__class_Oone [56, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.01/1.63 v_r____ [57, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.01/1.63 c_Polynomial_Opoly [58, 2] (w:1, o:226, a:1, s:1, b:0),
% 1.01/1.63 c_Polynomial_Odegree [59, 2] (w:1, o:228, a:1, s:1, b:0),
% 1.01/1.63 c_Rings_Odvd__class_Odvd [61, 3] (w:1, o:252, a:1, s:1, b:0),
% 1.01/1.63 class_Fields_Ofield [65, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.01/1.63 c_Groups_Ominus__class_Ominus [66, 3] (w:1, o:253, a:1, s:1, b:0),
% 1.01/1.63 c_Rings_Oinverse__class_Odivide [67, 3] (w:1, o:254, a:1, s:1, b:0),
% 1.01/1.63
% 1.01/1.63 class_Rings_Olinordered__semidom [69, 1] (w:1, o:126, a:1, s:1, b:0)
% 1.01/1.63 ,
% 1.01/1.63 class_Rings_Oring__1 [70, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.01/1.63 class_Rings_Olinordered__idom [75, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.01/1.63 v_n [76, 0] (w:1, o:53, a:1, s:1, b:0),
% 1.01/1.63 v_p [77, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.01/1.63 v_q [78, 0] (w:1, o:23, a:1, s:1, b:0),
% 1.01/1.63 class_Rings_Ocomm__semiring__1 [79, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.01/1.63 class_Rings_Odvd [83, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.01/1.63 class_Rings_Ocomm__ring__1 [85, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.01/1.63 class_Groups_Omonoid__mult [88, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.01/1.63 class_Rings_Oidom [92, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.01/1.63 class_Power_Opower [93, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.01/1.63 class_Rings_Ono__zero__divisors [94, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.01/1.63
% 1.01/1.63 class_Rings_Oring__no__zero__divisors [95, 1] (w:1, o:153, a:1, s:1
% 1.01/1.63 , b:0),
% 1.01/1.63 class_Rings_Omult__zero [96, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.01/1.63 class_Rings_Ozero__neq__one [97, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.01/1.63 class_Rings_Oring__1__no__zero__divisors [98, 1] (w:1, o:155, a:1, s:
% 1.01/1.63 1, b:0),
% 1.01/1.63 class_Rings_Oring [100, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.01/1.63 class_Rings_Odivision__ring__inverse__zero [101, 1] (w:1, o:157, a:1
% 1.01/1.63 , s:1, b:0),
% 1.01/1.63 class_Rings_Odivision__ring [102, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.01/1.63 class_Groups_Ocomm__monoid__mult [103, 1] (w:1, o:159, a:1, s:1, b:0)
% 1.01/1.63 ,
% 1.01/1.63 class_Fields_Ofield__inverse__zero [104, 1] (w:1, o:135, a:1, s:1, b:
% 1.01/1.63 0),
% 1.01/1.63 class_Rings_Oordered__cancel__semiring [105, 1] (w:1, o:160, a:1, s:1
% 1.01/1.63 , b:0),
% 1.01/1.63 class_Rings_Oordered__ring [106, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.01/1.63 class_Rings_Oordered__semiring [107, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.01/1.63
% 1.01/1.63 class_Rings_Oordered__comm__semiring [108, 1] (w:1, o:163, a:1, s:1
% 1.01/1.63 , b:0),
% 1.01/1.63 class_Rings_Olinordered__ring__strict [109, 1] (w:1, o:124, a:1, s:1
% 1.01/1.63 , b:0),
% 1.01/1.63 class_Rings_Olinordered__ring [110, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.01/1.63 class_Fields_Olinordered__field__inverse__zero [111, 1] (w:1, o:136
% 1.01/1.63 , a:1, s:1, b:0),
% 1.01/1.63 class_Rings_Osemiring__0 [114, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.01/1.63 c_Nat_OSuc [116, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.01/1.63 class_Groups_Ozero [127, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.01/1.63 class_Groups_Oab__group__add [130, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.01/1.63 class_Int_Oring__char__0 [133, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.01/1.63 class_Rings_Ocomm__ring [135, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.01/1.64 class_Rings_Ocomm__semiring__0 [136, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.01/1.64
% 1.01/1.64 c_Orderings_Oord__class_Oless [139, 3] (w:1, o:249, a:1, s:1, b:0),
% 1.01/1.64 hBOOL [143, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.01/1.64 class_Rings_Olinordered__comm__semiring__strict [146, 1] (w:1, o:146
% 1.01/1.64 , a:1, s:1, b:0),
% 1.01/1.64 class_Rings_Olinordered__semiring__strict [147, 1] (w:1, o:147, a:1
% 1.01/1.64 , s:1, b:0),
% 1.01/1.64 class_Fields_Olinordered__field [148, 1] (w:1, o:137, a:1, s:1, b:0)
% 1.01/1.64 ,
% 1.01/1.64 class_Rings_Olinordered__semiring [150, 1] (w:1, o:148, a:1, s:1, b:0
% 1.01/1.64 ),
% 1.01/1.64 tc_Int_Oint [155, 0] (w:1, o:96, a:1, s:1, b:0),
% 1.01/1.64 class_Groups_Ogroup__add [156, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.01/1.64 class_Groups_Oordered__ab__group__add [157, 1] (w:1, o:171, a:1, s:1
% 1.01/1.64 , b:0),
% 1.01/1.64 class_Groups_Olinordered__ab__group__add [158, 1] (w:1, o:138, a:1
% 1.01/1.64 , s:1, b:0),
% 1.01/1.64 class_Groups_Oab__semigroup__mult [159, 1] (w:1, o:172, a:1, s:1, b:0
% 1.01/1.64 ),
% 1.01/1.64 class_Groups_Oone [160, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.01/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [162, 2] (w:1, o:
% 1.01/1.64 224, a:1, s:1, b:0),
% 1.01/1.64 class_Orderings_Opreorder [163, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.01/1.64 c_Power_Opower_Opower [164, 3] (w:1, o:255, a:1, s:1, b:0),
% 1.01/1.64 class_Orderings_Oord [167, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.01/1.64 tc_fun [168, 2] (w:1, o:235, a:1, s:1, b:0),
% 1.01/1.64 class_Orderings_Olinorder [169, 1] (w:1, o:144, a:1, s:1, b:0),
% 1.01/1.64 class_Orderings_Oorder [170, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.01/1.64 c_Polynomial_Opcompose [171, 3] (w:1, o:256, a:1, s:1, b:0),
% 1.01/1.64 class_RealVector_Oreal__normed__field [172, 1] (w:1, o:174, a:1, s:1
% 1.01/1.64 , b:0),
% 1.01/1.64 class_RealVector_Oreal__normed__algebra [178, 1] (w:1, o:175, a:1, s:
% 1.01/1.64 1, b:0),
% 1.01/1.64 c_Nat__Transfer_Otsub [183, 2] (w:1, o:236, a:1, s:1, b:0),
% 1.01/1.64 c_Polynomial_Opos__poly [184, 2] (w:1, o:237, a:1, s:1, b:0),
% 1.01/1.64 class_Lattices_Oboolean__algebra [185, 1] (w:1, o:177, a:1, s:1, b:0)
% 1.01/1.64 ,
% 1.01/1.64 c_Polynomial_Omonom [186, 3] (w:1, o:257, a:1, s:1, b:0),
% 1.01/1.64 class_Lattices_Oab__semigroup__idem__mult [187, 1] (w:1, o:176, a:1
% 1.01/1.64 , s:1, b:0),
% 1.01/1.64 class_Groups_Ominus [190, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.01/1.64 class_Groups_Ouminus [191, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.01/1.64 c_Groups_Osgn__class_Osgn [192, 2] (w:1, o:238, a:1, s:1, b:0),
% 1.01/1.64 c_Polynomial_Opoly__rec [193, 5] (w:1, o:367, a:1, s:1, b:0),
% 1.01/1.64 class_RealVector_Oreal__normed__vector [194, 1] (w:1, o:180, a:1, s:1
% 1.01/1.64 , b:0),
% 1.01/1.64 class_RealVector_Oreal__normed__algebra__1 [195, 1] (w:1, o:181, a:1
% 1.01/1.64 , s:1, b:0),
% 1.01/1.64 class_Groups_Osgn__if [196, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.01/1.64 class_RealVector_Oreal__normed__div__algebra [197, 1] (w:1, o:183, a:
% 1.01/1.64 1, s:1, b:0),
% 1.01/1.64 c_fequal [198, 2] (w:1, o:239, a:1, s:1, b:0),
% 1.01/1.64 c_If [199, 4] (w:1, o:307, a:1, s:1, b:0),
% 1.01/1.64 c_Polynomial_Osynthetic__div [201, 3] (w:1, o:258, a:1, s:1, b:0),
% 1.01/1.64 c_Groups_Oplus__class_Oplus [202, 3] (w:1, o:259, a:1, s:1, b:0),
% 1.01/1.64 c_Polynomial_Ocoeff [203, 2] (w:1, o:227, a:1, s:1, b:0),
% 1.01/1.64 c_Int_Onumber__class_Onumber__of [205, 2] (w:1, o:240, a:1, s:1, b:0)
% 1.01/1.64 ,
% 1.01/1.64 class_Groups_Oordered__ab__semigroup__add__imp__le [206, 1] (w:1, o:
% 1.01/1.64 184, a:1, s:1, b:0),
% 1.01/1.64 class_Groups_Oordered__ab__semigroup__add [207, 1] (w:1, o:185, a:1
% 1.01/1.64 , s:1, b:0),
% 1.01/1.64 class_Groups_Ocomm__monoid__add [208, 1] (w:1, o:186, a:1, s:1, b:0)
% 1.01/1.64 ,
% 1.01/1.64 class_Int_Onumber [210, 1] (w:1, o:187, a:1, s:1, b:0),
% 1.01/1.64 class_Groups_Oordered__cancel__ab__semigroup__add [211, 1] (w:1, o:
% 1.01/1.64 188, a:1, s:1, b:0),
% 1.01/1.64 class_Int_Onumber__ring [212, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.01/1.64 class_Groups_Oordered__comm__monoid__add [213, 1] (w:1, o:190, a:1
% 1.01/1.64 , s:1, b:0),
% 1.01/1.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.01/1.64 214, 1] (w:1, o:193, a:1, s:1, b:0),
% 1.01/1.64 class_Groups_Ocancel__semigroup__add [216, 1] (w:1, o:194, a:1, s:1
% 1.01/1.64 , b:0),
% 1.01/1.64 class_Groups_Ocancel__ab__semigroup__add [217, 1] (w:1, o:195, a:1
% 1.01/1.64 , s:1, b:0),
% 1.01/1.64 class_Groups_Oab__semigroup__add [218, 1] (w:1, o:196, a:1, s:1, b:0)
% 1.01/1.64 ,
% 1.01/1.64 class_Groups_Omonoid__add [219, 1] (w:1, o:197, a:1, s:1, b:0),
% 1.01/1.64 class_Rings_Osemiring [221, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.01/1.64 class_Rings_Ocomm__semiring [222, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.01/1.64 class_Rings_Olinordered__semiring__1 [226, 1] (w:1, o:149, a:1, s:1
% 1.01/1.64 , b:0),
% 1.01/1.64 class_Rings_Olinordered__semiring__1__strict [227, 1] (w:1, o:150, a:
% 1.01/1.64 1, s:1, b:0),
% 1.01/1.64 class_RealVector_Oreal__field [229, 1] (w:1, o:192, a:1, s:1, b:0),
% 1.01/1.64 c_Polynomial_Opdivmod__rel [231, 5] (w:1, o:368, a:1, s:1, b:0),
% 1.01/1.64 class_Groups_Ocancel__comm__monoid__add [242, 1] (w:1, o:198, a:1, s:
% 1.01/1.64 1, b:0),
% 1.01/1.64 tc_HOL_Obool [244, 0] (w:1, o:95, a:1, s:1, b:0),
% 1.01/1.64 alpha1 [245, 3] (w:1, o:260, a:1, s:1, b:1),
% 1.01/1.64 alpha2 [246, 3] (w:1, o:271, a:1, s:1, b:1),
% 1.01/1.64 alpha3 [247, 3] (w:1, o:282, a:1, s:1, b:1),
% 1.01/1.64 alpha4 [248, 3] (w:1, o:291, a:1, s:1, b:1),
% 1.01/1.64 alpha5 [249, 3] (w:1, o:294, a:1, s:1, b:1),
% 1.01/1.64 alpha6 [250, 3] (w:1, o:295, a:1, s:1, b:1),
% 1.01/1.64 alpha7 [251, 2] (w:1, o:243, a:1, s:1, b:1),
% 3.59/3.97 alpha8 [252, 2] (w:1, o:244, a:1, s:1, b:1),
% 3.59/3.97 alpha9 [253, 4] (w:1, o:317, a:1, s:1, b:1),
% 3.59/3.97 alpha10 [254, 4] (w:1, o:318, a:1, s:1, b:1),
% 3.59/3.97 alpha11 [255, 3] (w:1, o:263, a:1, s:1, b:1),
% 3.59/3.97 alpha12 [256, 3] (w:1, o:264, a:1, s:1, b:1),
% 3.59/3.97 alpha13 [257, 2] (w:1, o:245, a:1, s:1, b:1),
% 3.59/3.97 alpha14 [258, 3] (w:1, o:265, a:1, s:1, b:1),
% 3.59/3.97 alpha15 [259, 3] (w:1, o:266, a:1, s:1, b:1),
% 3.59/3.97 alpha16 [260, 3] (w:1, o:267, a:1, s:1, b:1),
% 3.59/3.97 alpha17 [261, 3] (w:1, o:268, a:1, s:1, b:1),
% 3.59/3.97 alpha18 [262, 3] (w:1, o:269, a:1, s:1, b:1),
% 3.59/3.97 alpha19 [263, 3] (w:1, o:270, a:1, s:1, b:1),
% 3.59/3.97 alpha20 [264, 3] (w:1, o:272, a:1, s:1, b:1),
% 3.59/3.97 alpha21 [265, 3] (w:1, o:273, a:1, s:1, b:1),
% 3.59/3.97 alpha22 [266, 3] (w:1, o:274, a:1, s:1, b:1),
% 3.59/3.97 alpha23 [267, 3] (w:1, o:275, a:1, s:1, b:1),
% 3.59/3.97 alpha24 [268, 3] (w:1, o:276, a:1, s:1, b:1),
% 3.59/3.97 alpha25 [269, 3] (w:1, o:277, a:1, s:1, b:1),
% 3.59/3.97 alpha26 [270, 3] (w:1, o:278, a:1, s:1, b:1),
% 3.59/3.97 alpha27 [271, 3] (w:1, o:279, a:1, s:1, b:1),
% 3.59/3.97 alpha28 [272, 3] (w:1, o:280, a:1, s:1, b:1),
% 3.59/3.97 alpha29 [273, 3] (w:1, o:281, a:1, s:1, b:1),
% 3.59/3.97 alpha30 [274, 3] (w:1, o:283, a:1, s:1, b:1),
% 3.59/3.97 alpha31 [275, 3] (w:1, o:284, a:1, s:1, b:1),
% 3.59/3.97 alpha32 [276, 2] (w:1, o:246, a:1, s:1, b:1),
% 3.59/3.97 alpha33 [277, 2] (w:1, o:247, a:1, s:1, b:1),
% 3.59/3.97 alpha34 [278, 3] (w:1, o:285, a:1, s:1, b:1),
% 3.59/3.97 alpha35 [279, 3] (w:1, o:286, a:1, s:1, b:1),
% 3.59/3.97 alpha36 [280, 3] (w:1, o:287, a:1, s:1, b:1),
% 3.59/3.97 alpha37 [281, 3] (w:1, o:288, a:1, s:1, b:1),
% 3.59/3.97 alpha38 [282, 3] (w:1, o:289, a:1, s:1, b:1),
% 3.59/3.97 alpha39 [283, 3] (w:1, o:290, a:1, s:1, b:1),
% 3.59/3.97 alpha40 [284, 4] (w:1, o:319, a:1, s:1, b:1),
% 3.59/3.97 alpha41 [285, 4] (w:1, o:320, a:1, s:1, b:1),
% 3.59/3.97 alpha42 [286, 4] (w:1, o:321, a:1, s:1, b:1),
% 3.59/3.97 alpha43 [287, 4] (w:1, o:322, a:1, s:1, b:1),
% 3.59/3.97 alpha44 [288, 3] (w:1, o:292, a:1, s:1, b:1),
% 3.59/3.97 alpha45 [289, 3] (w:1, o:293, a:1, s:1, b:1),
% 3.59/3.97 alpha46 [290, 4] (w:1, o:323, a:1, s:1, b:1),
% 3.59/3.97 alpha47 [291, 4] (w:1, o:324, a:1, s:1, b:1),
% 3.59/3.97 alpha48 [292, 4] (w:1, o:325, a:1, s:1, b:1),
% 3.59/3.97 alpha49 [293, 4] (w:1, o:326, a:1, s:1, b:1),
% 3.59/3.97 alpha50 [294, 4] (w:1, o:327, a:1, s:1, b:1),
% 3.59/3.97 alpha51 [295, 4] (w:1, o:328, a:1, s:1, b:1),
% 3.59/3.97 alpha52 [296, 4] (w:1, o:329, a:1, s:1, b:1),
% 3.59/3.97 alpha53 [297, 4] (w:1, o:330, a:1, s:1, b:1),
% 3.59/3.97 alpha54 [298, 4] (w:1, o:331, a:1, s:1, b:1),
% 3.59/3.97 alpha55 [299, 4] (w:1, o:332, a:1, s:1, b:1),
% 3.59/3.97 alpha56 [300, 4] (w:1, o:333, a:1, s:1, b:1),
% 3.59/3.97 alpha57 [301, 4] (w:1, o:334, a:1, s:1, b:1),
% 3.59/3.97 alpha58 [302, 4] (w:1, o:335, a:1, s:1, b:1),
% 3.59/3.97 alpha59 [303, 4] (w:1, o:336, a:1, s:1, b:1),
% 3.59/3.97 alpha60 [304, 4] (w:1, o:337, a:1, s:1, b:1),
% 3.59/3.97 alpha61 [305, 4] (w:1, o:338, a:1, s:1, b:1),
% 3.59/3.97 alpha62 [306, 3] (w:1, o:296, a:1, s:1, b:1),
% 3.59/3.97 alpha63 [307, 2] (w:1, o:241, a:1, s:1, b:1),
% 3.59/3.97 alpha64 [308, 2] (w:1, o:242, a:1, s:1, b:1),
% 3.59/3.97 alpha65 [309, 3] (w:1, o:297, a:1, s:1, b:1),
% 3.59/3.97 alpha66 [310, 3] (w:1, o:298, a:1, s:1, b:1),
% 3.59/3.97 alpha67 [311, 4] (w:1, o:339, a:1, s:1, b:1),
% 3.59/3.97 alpha68 [312, 4] (w:1, o:340, a:1, s:1, b:1),
% 3.59/3.97 alpha69 [313, 4] (w:1, o:341, a:1, s:1, b:1),
% 3.59/3.97 alpha70 [314, 4] (w:1, o:342, a:1, s:1, b:1),
% 3.59/3.97 alpha71 [315, 4] (w:1, o:343, a:1, s:1, b:1),
% 3.59/3.97 alpha72 [316, 4] (w:1, o:344, a:1, s:1, b:1),
% 3.59/3.97 alpha73 [317, 4] (w:1, o:345, a:1, s:1, b:1),
% 3.59/3.97 alpha74 [318, 4] (w:1, o:346, a:1, s:1, b:1),
% 3.59/3.97 alpha75 [319, 4] (w:1, o:347, a:1, s:1, b:1),
% 3.59/3.97 alpha76 [320, 4] (w:1, o:348, a:1, s:1, b:1),
% 3.59/3.97 alpha77 [321, 4] (w:1, o:349, a:1, s:1, b:1),
% 3.59/3.97 alpha78 [322, 4] (w:1, o:350, a:1, s:1, b:1),
% 3.59/3.97 alpha79 [323, 4] (w:1, o:351, a:1, s:1, b:1),
% 3.59/3.97 alpha80 [324, 3] (w:1, o:299, a:1, s:1, b:1),
% 3.59/3.97 alpha81 [325, 4] (w:1, o:308, a:1, s:1, b:1),
% 3.59/3.97 alpha82 [326, 4] (w:1, o:309, a:1, s:1, b:1),
% 3.59/3.97 alpha83 [327, 4] (w:1, o:310, a:1, s:1, b:1),
% 3.59/3.97 alpha84 [328, 4] (w:1, o:311, a:1, s:1, b:1),
% 36.26/36.65 alpha85 [329, 4] (w:1, o:312, a:1, s:1, b:1),
% 36.26/36.65 alpha86 [330, 4] (w:1, o:313, a:1, s:1, b:1),
% 36.26/36.65 alpha87 [331, 4] (w:1, o:314, a:1, s:1, b:1),
% 36.26/36.65 alpha88 [332, 4] (w:1, o:315, a:1, s:1, b:1),
% 36.26/36.65 alpha89 [333, 4] (w:1, o:316, a:1, s:1, b:1),
% 36.26/36.65 alpha90 [334, 4] (w:1, o:352, a:1, s:1, b:1),
% 36.26/36.65 alpha91 [335, 4] (w:1, o:353, a:1, s:1, b:1),
% 36.26/36.65 alpha92 [336, 4] (w:1, o:354, a:1, s:1, b:1),
% 36.26/36.65 alpha93 [337, 4] (w:1, o:355, a:1, s:1, b:1),
% 36.26/36.65 alpha94 [338, 4] (w:1, o:356, a:1, s:1, b:1),
% 36.26/36.65 alpha95 [339, 4] (w:1, o:357, a:1, s:1, b:1),
% 36.26/36.65 alpha96 [340, 4] (w:1, o:358, a:1, s:1, b:1),
% 36.26/36.65 alpha97 [341, 4] (w:1, o:359, a:1, s:1, b:1),
% 36.26/36.65 alpha98 [342, 4] (w:1, o:360, a:1, s:1, b:1),
% 36.26/36.65 alpha99 [343, 4] (w:1, o:361, a:1, s:1, b:1),
% 36.26/36.65 alpha100 [344, 4] (w:1, o:362, a:1, s:1, b:1),
% 36.26/36.65 alpha101 [345, 4] (w:1, o:363, a:1, s:1, b:1),
% 36.26/36.65 alpha102 [346, 4] (w:1, o:364, a:1, s:1, b:1),
% 36.26/36.65 alpha103 [347, 4] (w:1, o:365, a:1, s:1, b:1),
% 36.26/36.65 alpha104 [348, 4] (w:1, o:366, a:1, s:1, b:1),
% 36.26/36.65 alpha105 [349, 3] (w:1, o:261, a:1, s:1, b:1),
% 36.26/36.65 alpha106 [350, 3] (w:1, o:262, a:1, s:1, b:1),
% 36.26/36.65 skol1 [351, 2] (w:1, o:229, a:1, s:1, b:1),
% 36.26/36.65 skol2 [352, 0] (w:1, o:14, a:1, s:1, b:1),
% 36.26/36.65 skol3 [353, 0] (w:1, o:15, a:1, s:1, b:1),
% 36.26/36.65 skol4 [354, 0] (w:1, o:16, a:1, s:1, b:1),
% 36.26/36.65 skol5 [355, 0] (w:1, o:17, a:1, s:1, b:1),
% 36.26/36.65 skol6 [356, 2] (w:1, o:230, a:1, s:1, b:1),
% 36.26/36.65 skol7 [357, 2] (w:1, o:231, a:1, s:1, b:1),
% 36.26/36.65 skol8 [358, 1] (w:1, o:117, a:1, s:1, b:1),
% 36.26/36.65 skol9 [359, 3] (w:1, o:300, a:1, s:1, b:1),
% 36.26/36.65 skol10 [360, 2] (w:1, o:232, a:1, s:1, b:1),
% 36.26/36.65 skol11 [361, 3] (w:1, o:301, a:1, s:1, b:1),
% 36.26/36.65 skol12 [362, 3] (w:1, o:302, a:1, s:1, b:1),
% 36.26/36.65 skol13 [363, 3] (w:1, o:303, a:1, s:1, b:1),
% 36.26/36.65 skol14 [364, 2] (w:1, o:233, a:1, s:1, b:1),
% 36.26/36.65 skol15 [365, 2] (w:1, o:234, a:1, s:1, b:1),
% 36.26/36.65 skol16 [366, 3] (w:1, o:304, a:1, s:1, b:1),
% 36.26/36.65 skol17 [367, 3] (w:1, o:305, a:1, s:1, b:1),
% 36.26/36.65 skol18 [368, 3] (w:1, o:306, a:1, s:1, b:1).
% 36.26/36.65
% 36.26/36.65
% 36.26/36.65 Starting Search:
% 36.26/36.65
% 36.26/36.65 *** allocated 170857 integers for clauses
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65
% 36.26/36.65 Intermediate Status:
% 36.26/36.65 Generated: 2746
% 36.26/36.65 Kept: 2009
% 36.26/36.65 Inuse: 6
% 36.26/36.65 Deleted: 0
% 36.26/36.65 Deletedinuse: 0
% 36.26/36.65
% 36.26/36.65 *** allocated 256285 integers for clauses
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65 *** allocated 384427 integers for clauses
% 36.26/36.65 *** allocated 256285 integers for termspace/termends
% 36.26/36.65
% 36.26/36.65 Intermediate Status:
% 36.26/36.65 Generated: 8742
% 36.26/36.65 Kept: 4013
% 36.26/36.65 Inuse: 140
% 36.26/36.65 Deleted: 0
% 36.26/36.65 Deletedinuse: 0
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65 *** allocated 576640 integers for clauses
% 36.26/36.65 *** allocated 384427 integers for termspace/termends
% 36.26/36.65
% 36.26/36.65 Intermediate Status:
% 36.26/36.65 Generated: 13890
% 36.26/36.65 Kept: 6508
% 36.26/36.65 Inuse: 261
% 36.26/36.65 Deleted: 0
% 36.26/36.65 Deletedinuse: 0
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65
% 36.26/36.65 Intermediate Status:
% 36.26/36.65 Generated: 22063
% 36.26/36.65 Kept: 9056
% 36.26/36.65 Inuse: 311
% 36.26/36.65 Deleted: 0
% 36.26/36.65 Deletedinuse: 0
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65 *** allocated 576640 integers for termspace/termends
% 36.26/36.65 *** allocated 864960 integers for clauses
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65
% 36.26/36.65 Intermediate Status:
% 36.26/36.65 Generated: 30854
% 36.26/36.65 Kept: 11396
% 36.26/36.65 Inuse: 346
% 36.26/36.65 Deleted: 0
% 36.26/36.65 Deletedinuse: 0
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65
% 36.26/36.65 Intermediate Status:
% 36.26/36.65 Generated: 45150
% 36.26/36.65 Kept: 14570
% 36.26/36.65 Inuse: 365
% 36.26/36.65 Deleted: 1
% 36.26/36.65 Deletedinuse: 0
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65 *** allocated 864960 integers for termspace/termends
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65 *** allocated 1297440 integers for clauses
% 36.26/36.65
% 36.26/36.65 Intermediate Status:
% 36.26/36.65 Generated: 54054
% 36.26/36.65 Kept: 16627
% 36.26/36.65 Inuse: 457
% 36.26/36.65 Deleted: 4
% 36.26/36.65 Deletedinuse: 0
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65
% 36.26/36.65 Intermediate Status:
% 36.26/36.65 Generated: 62830
% 36.26/36.65 Kept: 18636
% 36.26/36.65 Inuse: 507
% 36.26/36.65 Deleted: 4
% 36.26/36.65 Deletedinuse: 0
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65 Resimplifying clauses:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65
% 36.26/36.65 Intermediate Status:
% 36.26/36.65 Generated: 68108
% 36.26/36.65 Kept: 20639
% 36.26/36.65 Inuse: 580
% 36.26/36.65 Deleted: 376
% 36.26/36.65 Deletedinuse: 0
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 36.26/36.65 Done
% 36.26/36.65
% 36.26/36.65 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 75686
% 157.54/158.04 Kept: 22657
% 157.54/158.04 Inuse: 657
% 157.54/158.04 Deleted: 376
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 *** allocated 1297440 integers for termspace/termends
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 *** allocated 1946160 integers for clauses
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 93210
% 157.54/158.04 Kept: 26151
% 157.54/158.04 Inuse: 732
% 157.54/158.04 Deleted: 376
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 124508
% 157.54/158.04 Kept: 28312
% 157.54/158.04 Inuse: 742
% 157.54/158.04 Deleted: 376
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 144754
% 157.54/158.04 Kept: 30359
% 157.54/158.04 Inuse: 762
% 157.54/158.04 Deleted: 376
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 159786
% 157.54/158.04 Kept: 33301
% 157.54/158.04 Inuse: 777
% 157.54/158.04 Deleted: 376
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 *** allocated 1946160 integers for termspace/termends
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 167207
% 157.54/158.04 Kept: 37201
% 157.54/158.04 Inuse: 792
% 157.54/158.04 Deleted: 376
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 170654
% 157.54/158.04 Kept: 39296
% 157.54/158.04 Inuse: 797
% 157.54/158.04 Deleted: 376
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 Resimplifying clauses:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 *** allocated 2919240 integers for clauses
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 186302
% 157.54/158.04 Kept: 42316
% 157.54/158.04 Inuse: 822
% 157.54/158.04 Deleted: 456
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 194992
% 157.54/158.04 Kept: 46648
% 157.54/158.04 Inuse: 837
% 157.54/158.04 Deleted: 456
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 198739
% 157.54/158.04 Kept: 48846
% 157.54/158.04 Inuse: 842
% 157.54/158.04 Deleted: 456
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 215156
% 157.54/158.04 Kept: 52172
% 157.54/158.04 Inuse: 862
% 157.54/158.04 Deleted: 456
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 234637
% 157.54/158.04 Kept: 55608
% 157.54/158.04 Inuse: 877
% 157.54/158.04 Deleted: 456
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 245883
% 157.54/158.04 Kept: 58599
% 157.54/158.04 Inuse: 887
% 157.54/158.04 Deleted: 456
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 Resimplifying clauses:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 252120
% 157.54/158.04 Kept: 60607
% 157.54/158.04 Inuse: 899
% 157.54/158.04 Deleted: 508
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 *** allocated 2919240 integers for termspace/termends
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 264354
% 157.54/158.04 Kept: 63175
% 157.54/158.04 Inuse: 907
% 157.54/158.04 Deleted: 508
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 *** allocated 4378860 integers for clauses
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 271587
% 157.54/158.04 Kept: 65521
% 157.54/158.04 Inuse: 927
% 157.54/158.04 Deleted: 508
% 157.54/158.04 Deletedinuse: 0
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 277488
% 157.54/158.04 Kept: 67524
% 157.54/158.04 Inuse: 949
% 157.54/158.04 Deleted: 509
% 157.54/158.04 Deletedinuse: 1
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 286176
% 157.54/158.04 Kept: 69716
% 157.54/158.04 Inuse: 967
% 157.54/158.04 Deleted: 509
% 157.54/158.04 Deletedinuse: 1
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 294595
% 157.54/158.04 Kept: 72859
% 157.54/158.04 Inuse: 987
% 157.54/158.04 Deleted: 509
% 157.54/158.04 Deletedinuse: 1
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 299787
% 157.54/158.04 Kept: 75278
% 157.54/158.04 Inuse: 992
% 157.54/158.04 Deleted: 509
% 157.54/158.04 Deletedinuse: 1
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 307620
% 157.54/158.04 Kept: 78394
% 157.54/158.04 Inuse: 1007
% 157.54/158.04 Deleted: 509
% 157.54/158.04 Deletedinuse: 1
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 320894
% 157.54/158.04 Kept: 80481
% 157.54/158.04 Inuse: 1022
% 157.54/158.04 Deleted: 509
% 157.54/158.04 Deletedinuse: 1
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 Resimplifying clauses:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 330918
% 157.54/158.04 Kept: 83114
% 157.54/158.04 Inuse: 1027
% 157.54/158.04 Deleted: 743
% 157.54/158.04 Deletedinuse: 2
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04
% 157.54/158.04 Intermediate Status:
% 157.54/158.04 Generated: 338943
% 157.54/158.04 Kept: 85630
% 157.54/158.04 Inuse: 1047
% 157.54/158.04 Deleted: 743
% 157.54/158.04 Deletedinuse: 2
% 157.54/158.04
% 157.54/158.04 Resimplifying inuse:
% 157.54/158.04 Done
% 157.54/158.04
% 157.54/158.04 RCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------