TSTP Solution File: SWW273+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW273+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:45 EDT 2022
% Result : Timeout 300.02s 300.41s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW273+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Mon Jun 6 03:45:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.95/1.60 *** allocated 10000 integers for termspace/termends
% 0.95/1.60 *** allocated 10000 integers for clauses
% 0.95/1.60 *** allocated 10000 integers for justifications
% 0.95/1.60 *** allocated 15000 integers for termspace/termends
% 0.95/1.60 *** allocated 22500 integers for termspace/termends
% 0.95/1.60 *** allocated 33750 integers for termspace/termends
% 0.95/1.60 Bliksem 1.12
% 0.95/1.60
% 0.95/1.60
% 0.95/1.60 Automatic Strategy Selection
% 0.95/1.60
% 0.95/1.60 *** allocated 50625 integers for termspace/termends
% 0.95/1.60 *** allocated 75937 integers for termspace/termends
% 0.95/1.60 *** allocated 113905 integers for termspace/termends
% 0.95/1.60
% 0.95/1.60 Clauses:
% 0.95/1.60
% 0.95/1.60 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.95/1.60 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.95/1.60 tc_Complex_Ocomplex ) ) }.
% 0.95/1.60 { ! v_k____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.60 { ! v_pa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.95/1.60 tc_Complex_Ocomplex ) ) }.
% 0.95/1.60 { ! v_na____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Oorder(
% 0.95/1.60 tc_Complex_Ocomplex, v_a____, v_pa____ ), v_na____ ) }.
% 0.95/1.60 { v_s____ = c_Polynomial_OpCons( tc_Complex_Ocomplex, v_k____,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.95/1.60 ) }.
% 0.95/1.60 { v_qa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.95/1.60 ( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.95/1.60 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.95/1.60 tc_Complex_Ocomplex ) ) ) ) ), v_r____ ) }.
% 0.95/1.60 { ! c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { v_pa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.95/1.60 ( tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.60 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.95/1.60 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.95/1.60 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.95/1.60 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 0.95/1.60 , v_s____ ) }.
% 0.95/1.60 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_pa____ ) = v_na____ }.
% 0.95/1.60 { v_pa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.95/1.60 ( tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.60 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.95/1.60 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.95/1.60 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.95/1.60 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 0.95/1.60 , skol2 ) }.
% 0.95/1.60 { v_qa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.95/1.60 ( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.95/1.60 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.95/1.60 tc_Complex_Ocomplex ) ) ) ) ), skol3 ) }.
% 0.95/1.60 { ! v_s____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.95/1.60 tc_Complex_Ocomplex ) ) }.
% 0.95/1.60 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 0.95/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.95/1.60 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.95/1.60 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.95/1.60 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 0.95/1.60 v_a____, v_pa____ ) ), v_pa____ ) }.
% 0.95/1.60 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.95/1.60 tc_Complex_Ocomplex ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.95/1.60 tc_Complex_Ocomplex ), v_pa____, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.60 ( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_qa____ ), v_na____ ) )
% 0.95/1.60 }.
% 0.95/1.60 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 0.95/1.60 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus
% 0.95/1.60 ( tc_Complex_Ocomplex, v_a____ ), c_Polynomial_OpCons(
% 0.95/1.60 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.95/1.60 ) ), v_qa____ ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Oorder(
% 0.95/1.60 tc_Complex_Ocomplex, X, v_pa____ ), v_na____ ) }.
% 0.95/1.60 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.60 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.60 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.95/1.60 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.60 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.60 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.95/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.95/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.60 { ! v_n = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_s____ ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) = v_n }.
% 0.95/1.60 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_a____ ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.60 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.95/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_qa____ ), X ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.95/1.60 c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.60 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 0.95/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.60 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.60 ( X ), Z, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X )
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree
% 0.95/1.60 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.60 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.95/1.60 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.95/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.60 ), T ), U ), Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.60 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.95/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Nat_Onat ) ) = Y }.
% 0.95/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.95/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.95/1.60 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.95/1.60 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.60 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.95/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.95/1.60 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.95/1.60 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.60 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha1( X, Y, Z ), alpha24
% 0.95/1.60 ( X, Y, Z ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha1( X, Y, Z
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.95/1.60 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha24( X, Y, Z
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.95/1.60 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ), Y ), alpha24( X, Y, Z ) }.
% 0.95/1.60 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.60 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha1( X, Y, Z ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha2( X, Y, Z ), alpha25
% 0.95/1.60 ( X, Y, Z ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha2( X, Y, Z
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha25( X, Y, Z
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.95/1.60 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha25( X, Y, Z ) }.
% 0.95/1.61 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.61 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.95/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.61 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.95/1.61 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.95/1.61 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.95/1.61 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.95/1.61 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.95/1.61 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.95/1.61 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.61 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.95/1.61 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.61 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.95/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.95/1.61 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.61 = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.61 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.95/1.61 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.95/1.61 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.95/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.95/1.61 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.95/1.61 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.95/1.61 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha26( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha3( X, Y, Z ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha26( X, Y, Z, T ), !
% 0.95/1.61 alpha3( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.95/1.61 { ! alpha26( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.95/1.61 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha26( X, Y, Z, T ) }.
% 0.95/1.61 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha26(
% 0.95/1.61 X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha3( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.95/1.61 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha27( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha4( X, Y, T ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha27( X, Y, Z, T ), !
% 0.95/1.61 alpha4( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.95/1.61 { ! alpha27( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.95/1.61 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha27( X, Y, Z, T ) }.
% 0.95/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha27(
% 0.95/1.61 X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha4( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { Y = c_Groups_Ozero__class_Ozero( X ), alpha4( X, Y, Z ) }.
% 0.95/1.61 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha4( X, Y, Z ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.61 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.95/1.61 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.95/1.61 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.95/1.61 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 0.95/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.95/1.61 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.95/1.61 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.95/1.61 tc_Complex_Ocomplex ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder(
% 0.95/1.61 tc_Complex_Ocomplex, v_a____, v_pa____ ) ) ), v_pa____ ) }.
% 0.95/1.61 { v_s____ = c_Polynomial_OpCons( tc_Complex_Ocomplex, skol4,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.95/1.61 ) }.
% 0.95/1.61 { v_s____ = c_Polynomial_OpCons( tc_Complex_Ocomplex, skol5,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.95/1.61 ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.95/1.61 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.61 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.95/1.61 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.95/1.61 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.61 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.95/1.61 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.95/1.61 , Y ), X ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.95/1.61 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.95/1.61 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.95/1.61 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.95/1.61 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.95/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ) }.
% 0.95/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ) }.
% 0.95/1.61 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.95/1.61 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.95/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.61 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.95/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.95/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.95/1.61 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.95/1.61 { ! c_Nat_OSuc( X ) = X }.
% 0.95/1.61 { ! X = c_Nat_OSuc( X ) }.
% 0.95/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.95/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.95/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.61 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.61 ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.95/1.61 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.95/1.61 }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.95/1.61 c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.95/1.61 , c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.95/1.61 .
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.95/1.61 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.95/1.61 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.95/1.61 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.95/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.95/1.61 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.95/1.61 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.95/1.61 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.95/1.61 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.61 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.61 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.95/1.61 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.95/1.61 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.95/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.95/1.61 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.95/1.61 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.61 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), Y ), Z = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.95/1.61 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 0.95/1.61 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.61 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.95/1.61 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.95/1.61 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.95/1.61 .
% 0.95/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.95/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.95/1.61 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.95/1.61 .
% 0.95/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.95/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.95/1.61 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.61 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.95/1.61 Z, T ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ) ) = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.95/1.61 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.95/1.61 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.61 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.61 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.61 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.95/1.61 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.61 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.95/1.61 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.61 ) ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.61 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.61 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.61 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.95/1.61 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.61 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.61 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.61 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.95/1.61 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.95/1.61 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.95/1.61 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.95/1.61 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.95/1.61 , Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.95/1.61 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.95/1.61 , Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.95/1.61 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.95/1.61 ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.61 ), Y ) }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.61 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.95/1.61 Y ) ) ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.61 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.95/1.61 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.61 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.95/1.61 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.95/1.61 Y ) ) ), Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha5( X, Y
% 0.95/1.61 , Z ), alpha28( X, Y, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha28( X, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha28( X, Y, Z ) }.
% 0.95/1.61 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.61 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha5( X, Y, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) ), alpha6( X, Y, Z ), alpha29( X, Y, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha29( X, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) ) }.
% 0.95/1.61 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ), Y ), alpha29( X, Y, Z ) }.
% 0.95/1.61 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.61 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha6( X, Y, Z ) }.
% 0.95/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.95/1.61 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.95/1.61 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), ! hAPP(
% 0.95/1.61 c_Polynomial_Opoly( tc_Complex_Ocomplex, Z ), skol6( T, Z ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.95/1.61 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.95/1.61 ), Z ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), hAPP(
% 0.95/1.61 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol6( Y, Z ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.95/1.61 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.95/1.61 ), Z ), X ) ) }.
% 0.95/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.95/1.61 ( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.61 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.61 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.95/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.95/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 X, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ), Y ) }.
% 0.95/1.61 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.95/1.61 X ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha7( X, Y ), Y = X }
% 0.95/1.61 .
% 0.95/1.61 { ! alpha7( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! alpha7( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! alpha7( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), alpha7( X, Y ) }.
% 0.95/1.61 { ! alpha8( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! alpha8( X, Y ), ! Y = X }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha8( X, Y ) }
% 0.95/1.61 .
% 0.95/1.61 { ! alpha8( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! alpha8( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), alpha8( X, Y ) }.
% 0.95/1.61 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Nat_Onat, Y, Z ) }.
% 0.95/1.61 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Nat_Onat, Y, Z ) }.
% 0.95/1.61 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.95/1.61 , Z ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.95/1.61 Z, Y ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Nat_Onat, Y, Z ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { alpha57( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.95/1.61 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.95/1.61 { alpha57( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.95/1.61 ( X, Y ), Z ) ) }.
% 0.95/1.61 { ! alpha57( X, Y, Z ), alpha59( X, Y, Z ), Z = Y }.
% 0.95/1.61 { ! alpha57( X, Y, Z ), alpha59( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! alpha59( X, Y, Z ), alpha57( X, Y, Z ) }.
% 0.95/1.61 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha57( X, Y, Z ) }.
% 0.95/1.61 { ! alpha59( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.95/1.61 }.
% 0.95/1.61 { ! alpha59( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.95/1.61 X, Y ), Z ) ), alpha59( X, Y, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Y, Z ) }.
% 0.95/1.61 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.95/1.61 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ), Z ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Z ), Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.95/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.95/1.61 ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.95/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.95/1.61 .
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.95/1.61 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.95/1.61 }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.95/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.95/1.61 X ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.95/1.61 .
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.95/1.61 .
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.95/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.95/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.95/1.61 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Y ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.61 , Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.95/1.61 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.61 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha9( X, Y, Z, T ),
% 0.95/1.61 alpha30( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha30( X, Y, Z, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha30( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.95/1.61 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha9( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha10( X, Y, Z, T ),
% 0.95/1.61 alpha31( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha31( X, Y, Z, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha31( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.61 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha10( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , Y, Z ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , Y, Z ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.95/1.61 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha11( X, Y, Z ), alpha32( X,
% 0.95/1.61 Y, Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha11( X, Y, Z
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), alpha32( X, Y, Z ) }.
% 0.95/1.61 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.61 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), alpha11( X, Y, Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha12( X, Y, Z ), alpha33
% 0.95/1.61 ( X, Y, Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha12( X, Y, Z
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha33( X, Y, Z
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.95/1.61 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), alpha33( X, Y, Z ) }.
% 0.95/1.61 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.61 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), alpha12( X, Y, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha13( X, Y ) }.
% 0.95/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { ! alpha13( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.61 c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { ! alpha13( X, Y ), Y = c_Nat_OSuc( skol7( Z, Y ) ) }.
% 0.95/1.61 { ! alpha13( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol7( X,
% 0.95/1.61 Y ), X ) }.
% 0.95/1.61 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.95/1.61 ), alpha13( X, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol8( X ) ) }.
% 0.95/1.61 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.95/1.61 .
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.95/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.95/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 Y ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.61 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.61 ), X ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.95/1.61 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.95/1.61 }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.95/1.61 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.95/1.61 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.95/1.61 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.95/1.61 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.95/1.61 Y ), Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.61 Z, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.61 Z, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.95/1.61 Y ), Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.95/1.61 Y ), Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.61 Z, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.95/1.61 Z ), Y ), alpha34( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.95/1.61 Z ), Y ), alpha43( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha34( X, Y, Z
% 0.95/1.61 , T ), ! alpha43( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.95/1.61 { ! alpha43( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), alpha49( X, Y, Z, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.61 , alpha43( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha49( X, Y, Z, T ), alpha43( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha49( X, Y, Z, T ), alpha53( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha49( X, Y, Z, T ), alpha14( X, Y, Z ) }.
% 0.95/1.61 { ! alpha53( X, Y, Z, T ), ! alpha14( X, Y, Z ), alpha49( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha53( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 alpha53( X, Y, Z, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha53( X, Y, Z, T )
% 0.95/1.61 }.
% 0.95/1.61 { ! alpha34( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.61 alpha34( X, Y, Z, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha34( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 , alpha14( X, Y, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.95/1.61 , alpha14( X, Y, Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.61 Z, Y ) ), alpha35( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.61 Z, Y ) ), alpha44( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z
% 0.95/1.61 , T ), ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.95/1.61 { ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha50( X, Y, Z, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.95/1.61 , alpha44( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha50( X, Y, Z, T ), alpha44( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha50( X, Y, Z, T ), alpha54( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha50( X, Y, Z, T ), alpha15( X, Y, T ) }.
% 0.95/1.61 { ! alpha54( X, Y, Z, T ), ! alpha15( X, Y, T ), alpha50( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha54( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 alpha54( X, Y, Z, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha54( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha35( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 alpha35( X, Y, Z, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha35( X, Y, Z, T )
% 0.95/1.61 }.
% 0.95/1.61 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 , alpha15( X, Y, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 , alpha15( X, Y, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.95/1.61 ) ) = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.95/1.61 ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.95/1.61 ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.95/1.61 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.61 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.95/1.61 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.95/1.61 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.61 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.61 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.95/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , T, Y ), Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.95/1.61 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.95/1.61 ( X, Z, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.95/1.61 ( X, Z, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , T, Y ), Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , T, Y ), Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.95/1.61 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.95/1.61 ( X, Z, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , T, Z ), Y ), alpha36( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.95/1.61 , T, Z ), Y ), alpha45( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 0.95/1.61 , T ), ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.95/1.61 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), alpha51( X, Y, Z, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.61 , alpha45( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha51( X, Y, Z, T ), alpha45( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha51( X, Y, Z, T ), alpha55( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha51( X, Y, Z, T ), alpha16( X, Y, Z ) }.
% 0.95/1.61 { ! alpha55( X, Y, Z, T ), ! alpha16( X, Y, Z ), alpha51( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha55( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 alpha55( X, Y, Z, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha55( X, Y, Z, T )
% 0.95/1.61 }.
% 0.95/1.61 { ! alpha36( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.61 alpha36( X, Y, Z, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha36( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 , alpha16( X, Y, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Y ), alpha16( X, Y, Z ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.95/1.61 ( X, Z, Y ) ), alpha37( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.95/1.61 ( X, Z, Y ) ), alpha46( X, Y, Z, T ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z
% 0.95/1.61 , T ), ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.95/1.61 { ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha52( X, Y, Z, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.95/1.61 , alpha46( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha52( X, Y, Z, T ), alpha46( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha52( X, Y, Z, T ), alpha56( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha52( X, Y, Z, T ), alpha17( X, Y, T ) }.
% 0.95/1.61 { ! alpha56( X, Y, Z, T ), ! alpha17( X, Y, T ), alpha52( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha56( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 alpha56( X, Y, Z, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha56( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha37( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.61 alpha37( X, Y, Z, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha37( X, Y, Z, T )
% 0.95/1.61 }.
% 0.95/1.61 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.61 , alpha17( X, Y, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) ), alpha17( X, Y, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.61 ( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.95/1.61 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.95/1.61 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.95/1.61 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.95/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) }.
% 0.95/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.61 = Y }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.95/1.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.95/1.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.95/1.61 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Nat_Onat, Z, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.95/1.61 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), Y ) }.
% 0.95/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.95/1.61 ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.95/1.61 X ) ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Int_Oint, Z, X ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.95/1.61 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.95/1.61 ) }.
% 0.95/1.61 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.95/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.95/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.95/1.61 .
% 0.95/1.61 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.61 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.61 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.61 tc_Nat_Onat ), X ), Y ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.95/1.61 c_Polynomial_Odegree( X, Y ) ) }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.95/1.61 , Y ) }.
% 0.95/1.61 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.95/1.61 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 0.95/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.61 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.95/1.61 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.95/1.61 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.95/1.61 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.61 hAPP( Y, U ) ) }.
% 0.95/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.95/1.61 ( Z, skol9( X, Y, Z ) ), hAPP( Y, skol9( X, Y, Z ) ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.61 hAPP( Y, U ) ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.95/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.95/1.61 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.61 hAPP( Y, U ) ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.61 Y ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 Y ), ! Z = Y }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.61 Z ), ! Z = Y }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.61 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.61 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.61 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.61 , ! Z = Y }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.61 , ! Z = Y }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.61 , ! Y = Z }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.95/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.95/1.61 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.61 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.61 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), !
% 0.95/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ),
% 0.95/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.61 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.61 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.61 , ! Z = Y }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.61 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.61 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.61 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.95/1.61 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__field( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.61 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__field( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.95/1.61 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.95/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.95/1.61 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.95/1.61 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.95/1.61 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.95/1.61 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Int_Oint, Y, X ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.95/1.61 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.95/1.61 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.95/1.61 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.95/1.61 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.95/1.61 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.61 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.61 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__field( X ),
% 0.95/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.95/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.95/1.61 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.61 alpha18( X, Y, Z ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.61 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), ! alpha18( X, Y, Z ),
% 0.95/1.61 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.95/1.61 { ! alpha18( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.61 alpha18( X, Y, Z ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.95/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.95/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.95/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.95/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.95/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.95/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.95/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.95/1.62 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.95/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.95/1.62 ( tc_Int_Oint ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.95/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.95/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.95/1.62 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.95/1.62 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.95/1.62 .
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.95/1.62 ( tc_Int_Oint ) ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Int_Oint ), X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.62 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.95/1.62 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.62 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.95/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.95/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.95/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.95/1.62 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.95/1.62 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.95/1.62 hAPP( Z, Y ) ) }.
% 0.95/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, Y ), Z = Y }.
% 0.95/1.62 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, Y ) }.
% 0.95/1.62 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.95/1.62 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.62 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.95/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.95/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.95/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.95/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.95/1.62 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.95/1.62 ) ) }.
% 0.95/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.95/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.95/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.95/1.62 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.95/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.62 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.95/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.95/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.95/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.62 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.95/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.95/1.62 .
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Int_Oint ) ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Int_Oint ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.95/1.62 tc_Int_Oint, X, Y ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.95/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.62 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.95/1.62 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.95/1.62 X, Z ), Y ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.95/1.62 ( X ) ) ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.95/1.62 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.95/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.95/1.62 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.95/1.62 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.95/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.95/1.62 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.62 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.95/1.62 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.95/1.62 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.95/1.62 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.95/1.62 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.95/1.62 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.95/1.62 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.95/1.62 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.95/1.62 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.62 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.62 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.62 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.62 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.62 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.95/1.62 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.95/1.62 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.95/1.62 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.62 }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.95/1.62 tc_Int_Oint, X, Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol10( Z, Y ) ) ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.95/1.62 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.95/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.95/1.62 tc_Int_Oint, skol10( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.62 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.95/1.62 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.95/1.62 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.95/1.62 , Z ), X ) ) ) ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.95/1.62 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.95/1.62 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.95/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 skol11( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, skol11( X, T, U ),
% 0.95/1.62 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.62 , Y ) }.
% 0.95/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), skol11( X, Y, Z ) ), Z ), Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.95/1.62 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.95/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.95/1.62 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.95/1.62 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.95/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.62 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Int_Oint ) }.
% 0.95/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Int_Oint ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.95/1.62 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Nat_Onat ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.95/1.62 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.62 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.95/1.62 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.62 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 0.95/1.62 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 0.95/1.62 , Y ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.95/1.62 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.95/1.62 c_Polynomial_Ocoeff( X, Y ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.95/1.62 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol12( X
% 0.95/1.62 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol12( X, Y, Z ) ), Z =
% 0.95/1.62 Y }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.62 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Nat_Onat ) ) = Z }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.62 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.95/1.62 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.62 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.62 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.95/1.62 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.95/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.95/1.62 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.62 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.62 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.95/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.62 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.62 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.62 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.62 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.95/1.62 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.95/1.62 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.95/1.62 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.62 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.62 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.95/1.62 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.95/1.62 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.95/1.62 ( X ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.95/1.62 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.95/1.62 , skol13( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Polynomial_Odegree( X, Y ), Z ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol13( X
% 0.95/1.62 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.95/1.62 Y ), Z ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.62 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.62 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.95/1.62 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.95/1.62 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.95/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.95/1.62 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.62 , Y, T ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.62 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.62 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.62 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.62 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.95/1.62 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.62 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.62 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.62 ), ! U = T }.
% 0.95/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.62 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.62 ), ! Z = Y }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.95/1.62 ) ), Z ) }.
% 0.95/1.62 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.95/1.62 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.95/1.62 ) ), T ), Y ) }.
% 0.95/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.62 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.62 ), U = Z, T = Y }.
% 0.95/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.62 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.62 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.95/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.62 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.62 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.95/1.62 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.62 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 T, Y ), Z = Y }.
% 0.95/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 T, Y ) }.
% 0.95/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 Y, Z ), T = Y }.
% 0.95/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 Y, Z ) }.
% 0.95/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 T, Y ), Z = Y }.
% 0.95/1.62 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 T, Y ), Z = Y }.
% 0.95/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 Y, T ), Z = Y }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.95/1.62 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.95/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.62 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.62 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.95/1.62 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.62 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.95/1.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.95/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.95/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__field( X ),
% 0.95/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.62 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.95/1.62 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.62 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.62 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.62 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.62 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.95/1.62 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.95/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 Y, Z ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 Z, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.95/1.62 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.95/1.62 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.62 Y ) ) = Y }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 Z, Y ) ) = Y }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.95/1.62 ( X, T, Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.62 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.62 , Y, Z ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.62 ( X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.62 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.62 , T, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.62 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.62 , Y, T ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.62 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.62 , T, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.62 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.62 , T ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.95/1.62 ( X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.62 ( X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.62 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.62 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.62 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.62 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.62 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.62 X, Z, Y ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.95/1.62 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.95/1.62 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Y ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.95/1.62 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.95/1.62 X, Y ) ) }.
% 0.95/1.62 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.95/1.62 Z ) ), Y ) ) }.
% 0.95/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.95/1.62 Z ) ), U ), T ) = Y }.
% 0.95/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.95/1.62 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), U ), Y ) }.
% 0.95/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.62 W ) ), U ), Y ) }.
% 0.95/1.62 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.62 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), U ), Y ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.62 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.95/1.62 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.95/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.62 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.95/1.62 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.62 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.62 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.62 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.62 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.62 Z ) = Y }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.62 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, Z ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.62 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.62 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( X, Y ) }.
% 0.95/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 X ) }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.62 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.95/1.62 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.62 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.95/1.62 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.62 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.95/1.62 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.95/1.62 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.95/1.62 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.62 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.62 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.62 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.62 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.62 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.62 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.62 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.62 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.62 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.62 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.95/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.95/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.62 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.62 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.95/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.95/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.95/1.62 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.95/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( X, Z, W ) ), U ), Y ) ) }.
% 0.95/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.62 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.95/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.62 X, W, Z ) ), U ), T ), Y ) }.
% 0.95/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), Z ), U ), Y ) ) }.
% 0.95/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.95/1.62 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.95/1.62 hAPP( Z, skol14( U, W, Z ) ) ) }.
% 0.95/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.95/1.62 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.95/1.62 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol14( X
% 0.95/1.62 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.95/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.95/1.62 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.95/1.62 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol21( X,
% 0.95/1.62 Y, Z ) ) ) ) }.
% 0.95/1.62 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.95/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.95/1.62 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.95/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.95/1.62 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.95/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.95/1.62 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.95/1.62 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.95/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.95/1.62 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.95/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.95/1.62 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.95/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.95/1.62 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.95/1.62 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.95/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.95/1.62 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.95/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.95/1.62 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.62 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.95/1.62 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.62 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.95/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.62 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.95/1.62 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.62 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.62 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.95/1.62 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.95/1.62 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.95/1.62 ), Y ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.62 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.95/1.62 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.95/1.62 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.95/1.62 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.95/1.62 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.95/1.62 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.95/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.62 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.95/1.62 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.95/1.62 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.62 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Z, Y ), alpha60( X, Y, Z, T ), ! Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.62 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ), Z, Y ), alpha60( X, Y, Z, T ), ! hAPP(
% 0.95/1.62 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.95/1.62 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.95/1.62 .
% 0.95/1.62 { ! alpha60( X, Y, Z, T ), alpha61( X, Y, Z, T ), alpha58( X, Y, T ) }.
% 0.95/1.62 { ! alpha60( X, Y, Z, T ), alpha61( X, Y, Z, T ), ! hAPP(
% 0.95/1.62 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.62 { ! alpha61( X, Y, Z, T ), alpha60( X, Y, Z, T ) }.
% 0.95/1.62 { ! alpha58( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.95/1.62 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.62 alpha60( X, Y, Z, T ) }.
% 0.95/1.62 { ! alpha61( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.62 ( X ), Z, T ), alpha62( X, Y, Z, T ) }.
% 0.95/1.62 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha61( X, Y
% 0.95/1.62 , Z, T ) }.
% 0.95/1.62 { ! alpha62( X, Y, Z, T ), alpha61( X, Y, Z, T ) }.
% 0.95/1.62 { ! alpha62( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.95/1.62 ), skol15( X, Y, U, W ), Y ) }.
% 0.95/1.62 { ! alpha62( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.95/1.62 ), skol15( X, Y, U, T ), T ) }.
% 0.95/1.62 { ! alpha62( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.62 ( X ), skol15( X, Y, Z, T ), Z ) }.
% 0.95/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 0.95/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 0.95/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha62( X, Y
% 0.95/1.62 , Z, T ) }.
% 0.95/1.62 { ! alpha58( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! alpha58( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha58( X, Y, Z
% 0.95/1.62 ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.95/1.62 .
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.95/1.62 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.95/1.62 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.95/1.62 = X }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Int_Oint ) ) ) }.
% 0.95/1.62 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Int_Oint ) ) ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Int_Oint ), X ) = X }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Int_Oint ) ) = X }.
% 0.95/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.95/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Nat_Onat ) ) = X }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Nat_Onat ), X ) = X }.
% 0.95/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.62 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.95/1.62 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.62 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.62 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.62 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.95/1.62 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.95/1.62 , X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.95/1.62 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol16( X, Y ) ) }.
% 0.95/1.62 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol17( X, Y ) ) ) }.
% 0.95/1.62 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, X, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha19( X, Y ), alpha38( X
% 0.95/1.62 , Y ) }.
% 0.95/1.62 { ! alpha19( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.62 { ! alpha38( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.62 { ! alpha38( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { ! alpha38( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Nat_Onat ) ) }.
% 0.95/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha38( X, Y ) }.
% 0.95/1.62 { ! alpha19( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Nat_Onat ) ) }.
% 0.95/1.62 { ! alpha19( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha19( X, Y ) }.
% 0.95/1.62 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha20( X, Y ),
% 0.95/1.62 alpha39( X, Y ) }.
% 0.95/1.62 { ! alpha20( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.62 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.62 { ! alpha39( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.62 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.62 { ! alpha39( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { ! alpha39( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Nat_Onat ) ) }.
% 0.95/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha39( X, Y ) }.
% 0.95/1.62 { ! alpha20( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Nat_Onat ) ) }.
% 0.95/1.62 { ! alpha20( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha20( X, Y ) }.
% 0.95/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.62 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.95/1.62 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, Y ) ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, X ), Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.95/1.62 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.62 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.95/1.62 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.62 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.62 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, X ), Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, Y ), X ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.62 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.95/1.62 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.95/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.95/1.62 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.95/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.95/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.95/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.95/1.62 , Z ), X ) ), T ) ) }.
% 0.95/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.95/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.95/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, U, T ) ) }.
% 0.95/1.62 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.95/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.95/1.62 , ! alpha21( X, Y, Z ) }.
% 0.95/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.95/1.62 , ! alpha40( X, Y, Z ) }.
% 0.95/1.62 { alpha21( X, Y, Z ), alpha40( X, Y, Z ), hBOOL( hAPP( Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.95/1.62 { ! alpha40( X, Y, Z ), ! hBOOL( hAPP( Z, skol18( T, U, Z ) ) ) }.
% 0.95/1.62 { ! alpha40( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.62 skol18( X, Y, Z ) ) }.
% 0.95/1.62 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.95/1.62 ) ), alpha40( X, Y, Z ) }.
% 0.95/1.62 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.95/1.62 }.
% 0.95/1.62 { ! alpha21( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Nat_Onat ) ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha21( X, Y, Z ) }.
% 0.95/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.95/1.62 , alpha22( X, Y, Z ) }.
% 0.95/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.95/1.62 , alpha41( X, Y, Z ) }.
% 0.95/1.62 { ! alpha22( X, Y, Z ), ! alpha41( X, Y, Z ), hBOOL( hAPP( Z,
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.95/1.62 { ! alpha41( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.62 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.95/1.62 { ! hBOOL( hAPP( Z, skol19( T, U, Z ) ) ), alpha41( X, Y, Z ) }.
% 0.95/1.62 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol19( X, Y, Z ) ),
% 0.95/1.62 alpha41( X, Y, Z ) }.
% 0.95/1.62 { ! alpha22( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.95/1.62 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.95/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha22( X, Y, Z ) }
% 0.95/1.62 .
% 0.95/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha22
% 0.95/1.62 ( X, Y, Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Int_Oint ) ), X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.95/1.62 }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Int_Oint ) ), X ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.95/1.62 }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Int_Oint ) ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.95/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.95/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.62 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 0.95/1.62 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.95/1.62 c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.62 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.95/1.62 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.95/1.62 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.95/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.95/1.62 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.62 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.95/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.95/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.95/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.95/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.95/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.95/1.62 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.95/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.95/1.62 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.95/1.62 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.95/1.62 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.62 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.62 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.95/1.62 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.95/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.95/1.62 ( tc_Int_Oint ), Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.95/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.95/1.62 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.95/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.95/1.62 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.95/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.62 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.62 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.62 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.95/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.62 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.95/1.62 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.95/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.62 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.95/1.62 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.62 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.62 , alpha47( X, Y, Z, T ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.95/1.62 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha47( X, Y, Z, T ),
% 0.95/1.62 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.95/1.62 { ! alpha47( X, Y, Z, T ), alpha23( X, Z, T ) }.
% 0.95/1.62 { ! alpha47( X, Y, Z, T ), alpha42( X, Y, T ) }.
% 0.95/1.62 { ! alpha23( X, Z, T ), ! alpha42( X, Y, T ), alpha47( X, Y, Z, T ) }.
% 0.95/1.62 { ! alpha42( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), alpha48( X, Y, Z ) }.
% 0.95/1.62 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha42( X
% 0.95/1.62 , Y, Z ) }.
% 0.95/1.62 { ! alpha48( X, Y, Z ), alpha42( X, Y, Z ) }.
% 0.95/1.62 { ! alpha48( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.62 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha48( X
% 0.95/1.62 , Y, Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.95/1.62 ), c_Polynomial_Odegree( X, Z ) ), alpha48( X, Y, Z ) }.
% 0.95/1.62 { ! alpha23( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha23( X,
% 0.95/1.62 Y, Z ) }.
% 0.95/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha23( X
% 0.95/1.62 , Y, Z ) }.
% 0.95/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.95/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol20( X, Y ) ) }.
% 0.95/1.62 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.62 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.95/1.62 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.95/1.62 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.62 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.62 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.95/1.62 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.95/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.95/1.62 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.95/1.62 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.95/1.62 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.95/1.62 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.95/1.62 ( tc_fun( Y, X ) ) }.
% 0.95/1.62 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.95/1.62 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.95/1.62 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.95/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.62 tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.95/1.62 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.95/1.62 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.95/1.62 { class_Power_Opower( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.95/1.62 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.95/1.62 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.95/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.62 tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.95/1.62 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.95/1.62 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.95/1.62 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.95/1.62 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.95/1.62 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.95/1.62 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.95/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.62 tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.95/1.62 { ! class_Rings_Oidom( X ),
% 0.95/1.62 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.95/1.62 X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.95/1.62 ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.95/1.62 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.62 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.95/1.62 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.95/1.62 ( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.95/1.62 ( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.95/1.62 }.
% 0.95/1.62 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.95/1.62 ) ) }.
% 0.95/1.62 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.95/1.62 .
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.95/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.62 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.95/1.62 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.95/1.62 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.95/1.62 tc_Complex_Ocomplex ) ), v_qa____ ), v_na____ ) = hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.95/1.62 ), v_pa____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.62 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), hAPP( hAPP(
% 0.95/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.95/1.62 ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.95/1.62 c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex,
% 0.95/1.62 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), v_k____ ),
% 0.95/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.95/1.62 ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.95/1.62 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.95/1.62 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.95/1.62 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.95/1.62 tc_Complex_Ocomplex ) ) ) ) ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 0.95/1.62 , v_na____, c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ )
% 0.95/1.62 ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.95/1.62 tc_Complex_Ocomplex ) ), v_r____ ), v_na____ ) ) ) }.
% 0.95/1.62
% 0.95/1.62 *** allocated 15000 integers for clauses
% 0.95/1.62 *** allocated 22500 integers for clauses
% 0.95/1.62 *** allocated 33750 integers for clauses
% 0.95/1.62 *** allocated 50625 integers for clauses
% 0.95/1.62 *** allocated 75937 integers for clauses
% 0.95/1.62 percentage equality = 0.253801, percentage horn = 0.893822
% 0.95/1.62 This is a problem with some equality
% 0.95/1.62
% 0.95/1.62
% 0.95/1.62
% 0.95/1.62 Options Used:
% 0.95/1.62
% 0.95/1.62 useres = 1
% 0.95/1.62 useparamod = 1
% 0.95/1.62 useeqrefl = 1
% 0.95/1.62 useeqfact = 1
% 0.95/1.62 usefactor = 1
% 0.95/1.62 usesimpsplitting = 0
% 0.95/1.62 usesimpdemod = 5
% 0.95/1.62 usesimpres = 3
% 0.95/1.62
% 0.95/1.62 resimpinuse = 1000
% 0.95/1.62 resimpclauses = 20000
% 0.95/1.62 substype = eqrewr
% 0.95/1.62 backwardsubs = 1
% 0.95/1.62 selectoldest = 5
% 0.95/1.62
% 0.95/1.62 litorderings [0] = split
% 0.95/1.62 litorderings [1] = extend the termordering, first sorting on arguments
% 0.95/1.62
% 0.95/1.62 termordering = kbo
% 0.95/1.62
% 0.95/1.62 litapriori = 0
% 0.95/1.62 termapriori = 1
% 0.95/1.62 litaposteriori = 0
% 0.95/1.62 termaposteriori = 0
% 0.95/1.62 demodaposteriori = 0
% 0.95/1.62 ordereqreflfact = 0
% 0.95/1.62
% 0.95/1.62 litselect = negord
% 0.95/1.62
% 0.95/1.62 maxweight = 15
% 0.95/1.62 maxdepth = 30000
% 0.95/1.62 maxlength = 115
% 0.95/1.62 maxnrvars = 195
% 0.95/1.62 excuselevel = 1
% 0.95/1.62 increasemaxweight = 1
% 0.95/1.62
% 0.95/1.62 maxselected = 10000000
% 0.95/1.62 maxnrclauses = 10000000
% 0.95/1.62
% 0.95/1.62 showgenerated = 0
% 0.95/1.62 showkept = 0
% 0.95/1.62 showselected = 0
% 0.95/1.62 showdeleted = 0
% 0.95/1.62 showresimp = 1
% 0.95/1.62 showstatus = 2000
% 0.95/1.62
% 0.95/1.62 prologoutput = 0
% 0.95/1.62 nrgoals = 5000000
% 0.95/1.62 totalproof = 1
% 0.95/1.62
% 0.95/1.62 Symbols occurring in the translation:
% 0.95/1.62
% 0.95/1.62 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.95/1.62 . [1, 2] (w:1, o:200, a:1, s:1, b:0),
% 0.95/1.62 ! [4, 1] (w:0, o:115, a:1, s:1, b:0),
% 0.95/1.62 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.95/1.62 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.95/1.62 hAPP [38, 2] (w:1, o:224, a:1, s:1, b:0),
% 0.95/1.62 v_qa____ [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.95/1.62 tc_Complex_Ocomplex [40, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.95/1.62 tc_Polynomial_Opoly [41, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.95/1.62 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.95/1.62 v_k____ [43, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.95/1.62 v_pa____ [44, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.95/1.62 v_na____ [45, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.95/1.62 tc_Nat_Onat [46, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.95/1.62 v_a____ [47, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.95/1.62 c_Polynomial_Oorder [48, 3] (w:1, o:251, a:1, s:1, b:0),
% 0.95/1.62 c_Orderings_Oord__class_Oless__eq [49, 3] (w:1, o:249, a:1, s:1, b:0)
% 0.95/1.62 ,
% 0.95/1.62 v_s____ [50, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.95/1.62 c_Polynomial_OpCons [51, 3] (w:1, o:252, a:1, s:1, b:0),
% 0.95/1.62 c_Groups_Otimes__class_Otimes [52, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.95/1.62 c_Groups_Ouminus__class_Ouminus [53, 2] (w:1, o:226, a:1, s:1, b:0),
% 0.95/1.62
% 0.95/1.62 c_Groups_Oone__class_Oone [54, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.95/1.62 v_r____ [55, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.95/1.62 c_Power_Opower__class_Opower [56, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.95/1.62 c_Polynomial_Odegree [57, 2] (w:1, o:228, a:1, s:1, b:0),
% 0.95/1.62 c_Rings_Odvd__class_Odvd [60, 3] (w:1, o:253, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Oring__1 [64, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.95/1.62 class_Fields_Ofield [68, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.95/1.62 c_Rings_Oinverse__class_Odivide [69, 3] (w:1, o:254, a:1, s:1, b:0),
% 0.95/1.62
% 0.95/1.62 c_Groups_Ominus__class_Ominus [70, 3] (w:1, o:255, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Ocomm__semiring__1 [72, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.95/1.62 v_n [73, 0] (w:1, o:51, a:1, s:1, b:0),
% 0.95/1.62 v_p [74, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.95/1.62 c_Polynomial_Opoly [75, 2] (w:1, o:229, a:1, s:1, b:0),
% 0.95/1.62 class_Groups_Ozero [76, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.95/1.62 class_Groups_Oab__group__add [78, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Oidom [81, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.95/1.62 class_Groups_Omonoid__mult [83, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Olinordered__semidom [85, 1] (w:1, o:142, a:1, s:1, b:0)
% 0.95/1.62 ,
% 0.95/1.62 class_Fields_Olinordered__field__inverse__zero [87, 1] (w:1, o:132
% 0.95/1.62 , a:1, s:1, b:0),
% 0.95/1.62 class_Power_Opower [90, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Oring__1__no__zero__divisors [93, 1] (w:1, o:148, a:1, s:
% 0.95/1.62 1, b:0),
% 0.95/1.62 class_Rings_Omult__zero [95, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Ono__zero__divisors [96, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.95/1.62
% 0.95/1.62 class_Rings_Ozero__neq__one [97, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.95/1.62 class_Groups_Ocomm__monoid__mult [98, 1] (w:1, o:158, a:1, s:1, b:0)
% 0.95/1.62 ,
% 0.95/1.62 class_Fields_Ofield__inverse__zero [99, 1] (w:1, o:133, a:1, s:1, b:0
% 0.95/1.62 ),
% 0.95/1.62 class_Rings_Ocomm__semiring__0 [101, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.95/1.62
% 0.95/1.62 class_Rings_Osemiring__0 [107, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.95/1.62 c_Nat_OSuc [108, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Olinordered__idom [110, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.95/1.62 v_q [112, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.95/1.62 class_Int_Oring__char__0 [114, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Ocomm__ring [120, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Oring__no__zero__divisors [128, 1] (w:1, o:159, a:1, s:1
% 0.95/1.62 , b:0),
% 0.95/1.62 class_Rings_Oring [129, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Odivision__ring [130, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Odivision__ring__inverse__zero [131, 1] (w:1, o:166, a:1
% 0.95/1.62 , s:1, b:0),
% 0.95/1.62 class_Rings_Odvd [133, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Ocomm__ring__1 [134, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Olinordered__ring [135, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Olinordered__ring__strict [136, 1] (w:1, o:141, a:1, s:1
% 0.95/1.62 , b:0),
% 0.95/1.62 class_Rings_Oordered__cancel__semiring [137, 1] (w:1, o:168, a:1, s:1
% 0.95/1.62 , b:0),
% 0.95/1.62 class_Rings_Oordered__ring [138, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Oordered__semiring [139, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.95/1.62
% 0.95/1.62 class_Rings_Oordered__comm__semiring [140, 1] (w:1, o:171, a:1, s:1
% 0.95/1.62 , b:0),
% 0.95/1.62 c_Orderings_Oord__class_Oless [143, 3] (w:1, o:250, a:1, s:1, b:0),
% 0.95/1.62 class_Groups_Ogroup__add [146, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.95/1.62 class_Groups_Oordered__ab__group__add [147, 1] (w:1, o:173, a:1, s:1
% 0.95/1.62 , b:0),
% 0.95/1.62 class_Groups_Olinordered__ab__group__add [148, 1] (w:1, o:138, a:1
% 0.95/1.62 , s:1, b:0),
% 0.95/1.62 hBOOL [150, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Olinordered__comm__semiring__strict [154, 1] (w:1, o:150
% 0.95/1.62 , a:1, s:1, b:0),
% 0.95/1.62 class_Rings_Olinordered__semiring__strict [155, 1] (w:1, o:151, a:1
% 0.95/1.62 , s:1, b:0),
% 0.95/1.62 class_Fields_Olinordered__field [156, 1] (w:1, o:134, a:1, s:1, b:0)
% 0.95/1.62 ,
% 0.95/1.62 class_Rings_Olinordered__semiring [158, 1] (w:1, o:152, a:1, s:1, b:0
% 0.95/1.62 ),
% 0.95/1.62 class_Groups_Oab__semigroup__mult [159, 1] (w:1, o:175, a:1, s:1, b:0
% 0.95/1.62 ),
% 0.95/1.62 class_Groups_Oone [160, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.95/1.65 tc_Int_Oint [161, 0] (w:1, o:99, a:1, s:1, b:0),
% 0.95/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [162, 2] (w:1, o:
% 0.95/1.65 225, a:1, s:1, b:0),
% 0.95/1.65 class_Orderings_Opreorder [163, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.95/1.65 c_Power_Opower_Opower [164, 3] (w:1, o:256, a:1, s:1, b:0),
% 0.95/1.65 c_Polynomial_Opcompose [165, 3] (w:1, o:257, a:1, s:1, b:0),
% 0.95/1.65 class_Orderings_Oord [168, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.95/1.65 tc_fun [169, 2] (w:1, o:237, a:1, s:1, b:0),
% 0.95/1.65 class_Orderings_Olinorder [170, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.95/1.65 class_Orderings_Oorder [171, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.95/1.65 class_RealVector_Oreal__normed__field [172, 1] (w:1, o:177, a:1, s:1
% 0.95/1.65 , b:0),
% 0.95/1.65 class_RealVector_Oreal__normed__algebra [174, 1] (w:1, o:178, a:1, s:
% 0.95/1.65 1, b:0),
% 0.95/1.65 c_Polynomial_Opos__poly [178, 2] (w:1, o:238, a:1, s:1, b:0),
% 0.95/1.65 class_Lattices_Oboolean__algebra [179, 1] (w:1, o:180, a:1, s:1, b:0)
% 0.95/1.65 ,
% 0.95/1.65 class_Lattices_Oab__semigroup__idem__mult [184, 1] (w:1, o:179, a:1
% 0.95/1.65 , s:1, b:0),
% 0.95/1.65 class_Groups_Ominus [187, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.95/1.65 class_Groups_Ouminus [188, 1] (w:1, o:182, a:1, s:1, b:0),
% 0.95/1.65 c_Nat__Transfer_Otsub [190, 2] (w:1, o:239, a:1, s:1, b:0),
% 0.95/1.65 c_Polynomial_Omonom [191, 3] (w:1, o:258, a:1, s:1, b:0),
% 0.95/1.65 c_Groups_Osgn__class_Osgn [192, 2] (w:1, o:240, a:1, s:1, b:0),
% 0.95/1.65 class_RealVector_Oreal__normed__vector [193, 1] (w:1, o:183, a:1, s:1
% 0.95/1.65 , b:0),
% 0.95/1.65 class_RealVector_Oreal__normed__algebra__1 [194, 1] (w:1, o:184, a:1
% 0.95/1.65 , s:1, b:0),
% 0.95/1.65 class_Groups_Osgn__if [195, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.95/1.65 class_RealVector_Oreal__normed__div__algebra [196, 1] (w:1, o:186, a:
% 0.95/1.65 1, s:1, b:0),
% 0.95/1.65 c_Polynomial_Opoly__rec [197, 5] (w:1, o:327, a:1, s:1, b:0),
% 0.95/1.65 c_fequal [199, 2] (w:1, o:241, a:1, s:1, b:0),
% 0.95/1.65 c_If [200, 4] (w:1, o:299, a:1, s:1, b:0),
% 0.95/1.65 c_Polynomial_Osynthetic__div [201, 3] (w:1, o:259, a:1, s:1, b:0),
% 0.95/1.65 c_Polynomial_Ocoeff [202, 2] (w:1, o:227, a:1, s:1, b:0),
% 0.95/1.65 c_Groups_Oplus__class_Oplus [204, 3] (w:1, o:260, a:1, s:1, b:0),
% 0.95/1.65 c_Polynomial_Opoly__gcd [206, 3] (w:1, o:261, a:1, s:1, b:0),
% 0.95/1.65 class_Groups_Ocomm__monoid__add [207, 1] (w:1, o:187, a:1, s:1, b:0)
% 0.95/1.65 ,
% 0.95/1.65 class_Groups_Oordered__cancel__ab__semigroup__add [208, 1] (w:1, o:
% 0.95/1.65 188, a:1, s:1, b:0),
% 0.95/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.95/1.65 209, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.95/1.65 class_Groups_Omonoid__add [210, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.95/1.65 class_Rings_Ocomm__semiring [211, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.95/1.65 class_Rings_Osemiring [213, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.95/1.65 class_Groups_Oab__semigroup__add [214, 1] (w:1, o:193, a:1, s:1, b:0)
% 0.95/1.65 ,
% 0.95/1.65 class_Groups_Ocancel__semigroup__add [215, 1] (w:1, o:194, a:1, s:1
% 0.95/1.65 , b:0),
% 0.95/1.65 class_Groups_Ocancel__ab__semigroup__add [216, 1] (w:1, o:195, a:1
% 0.95/1.65 , s:1, b:0),
% 0.95/1.65 class_Groups_Oordered__comm__monoid__add [217, 1] (w:1, o:196, a:1
% 0.95/1.65 , s:1, b:0),
% 0.95/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le [218, 1] (w:1, o:
% 0.95/1.65 197, a:1, s:1, b:0),
% 0.95/1.65 class_Groups_Oordered__ab__semigroup__add [219, 1] (w:1, o:198, a:1
% 0.95/1.65 , s:1, b:0),
% 0.95/1.65 class_Rings_Olinordered__semiring__1 [224, 1] (w:1, o:153, a:1, s:1
% 0.95/1.65 , b:0),
% 0.95/1.65 class_Rings_Olinordered__semiring__1__strict [225, 1] (w:1, o:154, a:
% 0.95/1.65 1, s:1, b:0),
% 0.95/1.65 class_RealVector_Oreal__field [227, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.95/1.65 c_Polynomial_Opdivmod__rel [237, 5] (w:1, o:328, a:1, s:1, b:0),
% 0.95/1.65 class_Groups_Ocancel__comm__monoid__add [243, 1] (w:1, o:199, a:1, s:
% 0.95/1.65 1, b:0),
% 0.95/1.65 tc_HOL_Obool [245, 0] (w:1, o:98, a:1, s:1, b:0),
% 0.95/1.65 alpha1 [246, 3] (w:1, o:262, a:1, s:1, b:1),
% 0.95/1.65 alpha2 [247, 3] (w:1, o:270, a:1, s:1, b:1),
% 0.95/1.65 alpha3 [248, 3] (w:1, o:278, a:1, s:1, b:1),
% 0.95/1.65 alpha4 [249, 3] (w:1, o:281, a:1, s:1, b:1),
% 0.95/1.65 alpha5 [250, 3] (w:1, o:286, a:1, s:1, b:1),
% 0.95/1.65 alpha6 [251, 3] (w:1, o:290, a:1, s:1, b:1),
% 0.95/1.65 alpha7 [252, 2] (w:1, o:242, a:1, s:1, b:1),
% 0.95/1.65 alpha8 [253, 2] (w:1, o:243, a:1, s:1, b:1),
% 9.41/9.77 alpha9 [254, 4] (w:1, o:300, a:1, s:1, b:1),
% 9.41/9.77 alpha10 [255, 4] (w:1, o:301, a:1, s:1, b:1),
% 9.41/9.77 alpha11 [256, 3] (w:1, o:263, a:1, s:1, b:1),
% 9.41/9.77 alpha12 [257, 3] (w:1, o:264, a:1, s:1, b:1),
% 9.41/9.77 alpha13 [258, 2] (w:1, o:244, a:1, s:1, b:1),
% 9.41/9.77 alpha14 [259, 3] (w:1, o:265, a:1, s:1, b:1),
% 9.41/9.77 alpha15 [260, 3] (w:1, o:266, a:1, s:1, b:1),
% 9.41/9.77 alpha16 [261, 3] (w:1, o:267, a:1, s:1, b:1),
% 9.41/9.77 alpha17 [262, 3] (w:1, o:268, a:1, s:1, b:1),
% 9.41/9.77 alpha18 [263, 3] (w:1, o:269, a:1, s:1, b:1),
% 9.41/9.77 alpha19 [264, 2] (w:1, o:245, a:1, s:1, b:1),
% 9.41/9.77 alpha20 [265, 2] (w:1, o:246, a:1, s:1, b:1),
% 9.41/9.77 alpha21 [266, 3] (w:1, o:271, a:1, s:1, b:1),
% 9.41/9.77 alpha22 [267, 3] (w:1, o:272, a:1, s:1, b:1),
% 9.41/9.77 alpha23 [268, 3] (w:1, o:273, a:1, s:1, b:1),
% 9.41/9.77 alpha24 [269, 3] (w:1, o:274, a:1, s:1, b:1),
% 9.41/9.77 alpha25 [270, 3] (w:1, o:275, a:1, s:1, b:1),
% 9.41/9.77 alpha26 [271, 4] (w:1, o:302, a:1, s:1, b:1),
% 9.41/9.77 alpha27 [272, 4] (w:1, o:303, a:1, s:1, b:1),
% 9.41/9.77 alpha28 [273, 3] (w:1, o:276, a:1, s:1, b:1),
% 9.41/9.77 alpha29 [274, 3] (w:1, o:277, a:1, s:1, b:1),
% 9.41/9.77 alpha30 [275, 4] (w:1, o:304, a:1, s:1, b:1),
% 9.41/9.77 alpha31 [276, 4] (w:1, o:305, a:1, s:1, b:1),
% 9.41/9.77 alpha32 [277, 3] (w:1, o:279, a:1, s:1, b:1),
% 9.41/9.77 alpha33 [278, 3] (w:1, o:280, a:1, s:1, b:1),
% 9.41/9.77 alpha34 [279, 4] (w:1, o:306, a:1, s:1, b:1),
% 9.41/9.77 alpha35 [280, 4] (w:1, o:307, a:1, s:1, b:1),
% 9.41/9.77 alpha36 [281, 4] (w:1, o:308, a:1, s:1, b:1),
% 9.41/9.77 alpha37 [282, 4] (w:1, o:309, a:1, s:1, b:1),
% 9.41/9.77 alpha38 [283, 2] (w:1, o:247, a:1, s:1, b:1),
% 9.41/9.77 alpha39 [284, 2] (w:1, o:248, a:1, s:1, b:1),
% 9.41/9.77 alpha40 [285, 3] (w:1, o:282, a:1, s:1, b:1),
% 9.41/9.77 alpha41 [286, 3] (w:1, o:283, a:1, s:1, b:1),
% 9.41/9.77 alpha42 [287, 3] (w:1, o:284, a:1, s:1, b:1),
% 9.41/9.77 alpha43 [288, 4] (w:1, o:310, a:1, s:1, b:1),
% 9.41/9.77 alpha44 [289, 4] (w:1, o:311, a:1, s:1, b:1),
% 9.41/9.77 alpha45 [290, 4] (w:1, o:312, a:1, s:1, b:1),
% 9.41/9.77 alpha46 [291, 4] (w:1, o:313, a:1, s:1, b:1),
% 9.41/9.77 alpha47 [292, 4] (w:1, o:314, a:1, s:1, b:1),
% 9.41/9.77 alpha48 [293, 3] (w:1, o:285, a:1, s:1, b:1),
% 9.41/9.77 alpha49 [294, 4] (w:1, o:315, a:1, s:1, b:1),
% 9.41/9.77 alpha50 [295, 4] (w:1, o:316, a:1, s:1, b:1),
% 9.41/9.77 alpha51 [296, 4] (w:1, o:317, a:1, s:1, b:1),
% 9.41/9.77 alpha52 [297, 4] (w:1, o:318, a:1, s:1, b:1),
% 9.41/9.77 alpha53 [298, 4] (w:1, o:319, a:1, s:1, b:1),
% 9.41/9.77 alpha54 [299, 4] (w:1, o:320, a:1, s:1, b:1),
% 9.41/9.77 alpha55 [300, 4] (w:1, o:321, a:1, s:1, b:1),
% 9.41/9.77 alpha56 [301, 4] (w:1, o:322, a:1, s:1, b:1),
% 9.41/9.77 alpha57 [302, 3] (w:1, o:287, a:1, s:1, b:1),
% 9.41/9.77 alpha58 [303, 3] (w:1, o:288, a:1, s:1, b:1),
% 9.41/9.77 alpha59 [304, 3] (w:1, o:289, a:1, s:1, b:1),
% 9.41/9.77 alpha60 [305, 4] (w:1, o:323, a:1, s:1, b:1),
% 9.41/9.77 alpha61 [306, 4] (w:1, o:324, a:1, s:1, b:1),
% 9.41/9.77 alpha62 [307, 4] (w:1, o:325, a:1, s:1, b:1),
% 9.41/9.77 skol1 [308, 2] (w:1, o:230, a:1, s:1, b:1),
% 9.41/9.77 skol2 [309, 0] (w:1, o:14, a:1, s:1, b:1),
% 9.41/9.77 skol3 [310, 0] (w:1, o:15, a:1, s:1, b:1),
% 9.41/9.77 skol4 [311, 0] (w:1, o:16, a:1, s:1, b:1),
% 9.41/9.77 skol5 [312, 0] (w:1, o:17, a:1, s:1, b:1),
% 9.41/9.77 skol6 [313, 2] (w:1, o:231, a:1, s:1, b:1),
% 9.41/9.77 skol7 [314, 2] (w:1, o:232, a:1, s:1, b:1),
% 9.41/9.77 skol8 [315, 1] (w:1, o:120, a:1, s:1, b:1),
% 9.41/9.77 skol9 [316, 3] (w:1, o:291, a:1, s:1, b:1),
% 9.41/9.77 skol10 [317, 2] (w:1, o:233, a:1, s:1, b:1),
% 9.41/9.77 skol11 [318, 3] (w:1, o:292, a:1, s:1, b:1),
% 9.41/9.77 skol12 [319, 3] (w:1, o:293, a:1, s:1, b:1),
% 9.41/9.77 skol13 [320, 3] (w:1, o:294, a:1, s:1, b:1),
% 9.41/9.77 skol14 [321, 3] (w:1, o:295, a:1, s:1, b:1),
% 9.41/9.77 skol15 [322, 4] (w:1, o:326, a:1, s:1, b:1),
% 9.41/9.77 skol16 [323, 2] (w:1, o:234, a:1, s:1, b:1),
% 9.41/9.77 skol17 [324, 2] (w:1, o:235, a:1, s:1, b:1),
% 9.41/9.77 skol18 [325, 3] (w:1, o:296, a:1, s:1, b:1),
% 9.41/9.77 skol19 [326, 3] (w:1, o:297, a:1, s:1, b:1),
% 9.41/9.77 skol20 [327, 2] (w:1, o:236, a:1, s:1, b:1),
% 9.41/9.77 skol21 [328, 3] (w:1, o:298, a:1, s:1, b:1).
% 9.41/9.77
% 9.41/9.77
% 9.41/9.77 Starting Search:
% 9.41/9.77
% 9.41/9.77 *** allocated 113905 integers for clauses
% 9.41/9.77 *** allocated 170857 integers for clauses
% 9.41/9.77 Resimplifying inuse:
% 9.41/9.77 Done
% 9.41/9.77
% 9.41/9.77
% 9.41/9.77 Intermediate Status:
% 9.41/9.77 Generated: 2987
% 95.33/95.75 Kept: 2015
% 95.33/95.75 Inuse: 50
% 95.33/95.75 Deleted: 1
% 95.33/95.75 Deletedinuse: 0
% 95.33/95.75
% 95.33/95.75 *** allocated 256285 integers for clauses
% 95.33/95.75 *** allocated 170857 integers for termspace/termends
% 95.33/95.75 *** allocated 384427 integers for clauses
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 *** allocated 256285 integers for termspace/termends
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 8694
% 95.33/95.75 Kept: 4199
% 95.33/95.75 Inuse: 170
% 95.33/95.75 Deleted: 1
% 95.33/95.75 Deletedinuse: 0
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 *** allocated 576640 integers for clauses
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 *** allocated 384427 integers for termspace/termends
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 13310
% 95.33/95.75 Kept: 6217
% 95.33/95.75 Inuse: 299
% 95.33/95.75 Deleted: 8
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 21382
% 95.33/95.75 Kept: 8758
% 95.33/95.75 Inuse: 369
% 95.33/95.75 Deleted: 8
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 *** allocated 864960 integers for clauses
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 *** allocated 576640 integers for termspace/termends
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 28320
% 95.33/95.75 Kept: 11007
% 95.33/95.75 Inuse: 398
% 95.33/95.75 Deleted: 9
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 49466
% 95.33/95.75 Kept: 13506
% 95.33/95.75 Inuse: 461
% 95.33/95.75 Deleted: 11
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 *** allocated 1297440 integers for clauses
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 61308
% 95.33/95.75 Kept: 15610
% 95.33/95.75 Inuse: 491
% 95.33/95.75 Deleted: 11
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 *** allocated 864960 integers for termspace/termends
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 65531
% 95.33/95.75 Kept: 17760
% 95.33/95.75 Inuse: 506
% 95.33/95.75 Deleted: 11
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 70092
% 95.33/95.75 Kept: 19773
% 95.33/95.75 Inuse: 533
% 95.33/95.75 Deleted: 11
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 Resimplifying clauses:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 82253
% 95.33/95.75 Kept: 23560
% 95.33/95.75 Inuse: 551
% 95.33/95.75 Deleted: 525
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 *** allocated 1946160 integers for clauses
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 87636
% 95.33/95.75 Kept: 25628
% 95.33/95.75 Inuse: 566
% 95.33/95.75 Deleted: 525
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 94510
% 95.33/95.75 Kept: 28128
% 95.33/95.75 Inuse: 581
% 95.33/95.75 Deleted: 525
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 *** allocated 1297440 integers for termspace/termends
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 101208
% 95.33/95.75 Kept: 30141
% 95.33/95.75 Inuse: 604
% 95.33/95.75 Deleted: 525
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 110464
% 95.33/95.75 Kept: 32220
% 95.33/95.75 Inuse: 646
% 95.33/95.75 Deleted: 525
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 116892
% 95.33/95.75 Kept: 35498
% 95.33/95.75 Inuse: 656
% 95.33/95.75 Deleted: 525
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 122723
% 95.33/95.75 Kept: 37754
% 95.33/95.75 Inuse: 671
% 95.33/95.75 Deleted: 525
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 131331
% 95.33/95.75 Kept: 39781
% 95.33/95.75 Inuse: 690
% 95.33/95.75 Deleted: 525
% 95.33/95.75 Deletedinuse: 6
% 95.33/95.75
% 95.33/95.75 *** allocated 2919240 integers for clauses
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 Resimplifying clauses:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 145046
% 95.33/95.75 Kept: 42763
% 95.33/95.75 Inuse: 701
% 95.33/95.75 Deleted: 683
% 95.33/95.75 Deletedinuse: 7
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 150506
% 95.33/95.75 Kept: 44785
% 95.33/95.75 Inuse: 725
% 95.33/95.75 Deleted: 683
% 95.33/95.75 Deletedinuse: 7
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 157980
% 95.33/95.75 Kept: 46848
% 95.33/95.75 Inuse: 761
% 95.33/95.75 Deleted: 683
% 95.33/95.75 Deletedinuse: 7
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 171472
% 95.33/95.75 Kept: 48855
% 95.33/95.75 Inuse: 795
% 95.33/95.75 Deleted: 684
% 95.33/95.75 Deletedinuse: 8
% 95.33/95.75
% 95.33/95.75 *** allocated 1946160 integers for termspace/termends
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75 Resimplifying inuse:
% 95.33/95.75 Done
% 95.33/95.75
% 95.33/95.75
% 95.33/95.75 Intermediate Status:
% 95.33/95.75 Generated: 181362
% 95.33/95.75 Kept: 50935
% 95.33/95.75 Inuse: 851
% 95.33/95.75 Deleted: 68Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------